In the cases the question describes, a creature using a form-changing effect in this DM's campaigns sees its alternate form largely subsume its original form
In this DM's campaigns, when a creature assumes a new form, the assumed form's physical layout is always that of a typical creature of the assumed form's kind, no matter the original creature's appearance or if any parts are missing from the original creature or if any parts have been added to the original creature.
In other words, in this DM's campaigns, the original creature's form is completely replaced by that of the assumed form unless the form-changing effect specifies otherwise. No signs of injury on the original form transfer to the assumed form (although the hp damage remains) and a damaged limb (perhaps due to the Variant: Damage to Specific Area (Dungeon Master's Guide 27)) causes the creature no penalties in the assumed form (although, again, the hp damage remains). And, when the creature resumes its original form, signs of injury reappear, and penalties from the damaged limb resume.
For example, a creature that assumes the form of a cat (Monster Manual 270) assumes the form of a cat with all normal cat parts even if the creature's original form is, for whatever reason, missing an arm, leg, tail, head, or whatever. And it will also still be missing its arm, leg, tail, head, or whatever when the creature resumes its original form.
Likewise, the original form's haircut or mundane tattoos don't transfer to the assumed form. By the same token, if the creature receives in its assumed form a haircut or mundane tattoos, those won't be present when it resumes its original form… and that assumed form's haircut or mundane tattoos won't be present again when the creature assumes that form again after having assumed another form—including its original.1,2
To be clear, the supernatural ability alternate form, in part, says that the creature "assume[s] one or more specific alternate forms. This ability works much like the polymorph spell, except that the creature is limited to the forms specified…" (Monster Manual 305). Similarly, the supernatural ability change shape, in part, says that the creature "assume[s] the appearance of a specific creature or type of creature (usually a humanoid), but retains most of its own physical qualities" (306).3 The 4th-level Sor/Wiz spell polymorph [trans] (Player's Handbook 263) is like the 2nd-level Sor/Wiz spell alter self [trans] (197) therefore allowing a creature to "assume the form of a creature…. You can change into a member of your own kind or even into yourself."
And this DM has always ruled that when a creature uses one of these abilities or spells that the new form that the creature assumes is otherwise a typical creature like that found in the Monster Manual or elsewhere.4 This DM imagines any other ruling leading to anarchy.
That is, the creature can't opt to have the assumed form possess an arbitrary number of additional extremities, even if, for example, the campaign includes grafts (see Fiend Folio 207–15 et al.). Additionally, the creature can't pick to have the assumed form possess additional extremities like the extra arms granted by the 3rd-level Sor/Wiz spell girallon's blessing [trans] (Spell Compendium 106) or the intestinal tentacle/snake that's created with the 5th-level Sor/Wiz spell gutsnake [trans] (108). Finally, the assumed form can't possess transformed extremities like fiery wings instead of arms as if the form had been the subject of the 3rd-level Drd spell fire wings [trans] (93).
Similarly, the creature's assumed form can't have less than the average number of extremities. That is, despite perhaps once having seen an orc that possessed a snake tail instead of legs because that specific orc rolled 39–40 during a bout with the disease warp touch (Book of Vile Darkness 32), if the creature assumes that orc's form, the creature assumes that form as if it hadn't been so touched. Likewise, an assumed form can't be essentially the subject of a spell or special ability: this DM doesn't allow the creature to pick an assumed form that has the usual number arms but, for example, they're all totally swole as if the assumed form gained an arbitrary number of arms then was the subject of the 2nd-level Sor/Wiz spell fuse arms (SpC 100). Just no.
On this topic, this DM happens to agree with Skip Williams's Rules of the Game column "Polymorphing Revisited (Part Three)" on Physical Description that says
When a creature assumes a new form through the alternate form special quality, it gains… all the miscellaneous physical qualities that a typical specimen of the assumed form would have [including] basic things such as the number of and kinds of limbs and appendages the creature has, its height and weight, skin color, hair color, and the like.
When assuming a new form, the creature can freely designate any physical attributes that normally vary between individuals of the assumed form's kind. In most cases, this means the creature can set the assumed form's hair or skin color, eye color, height and weight, and similar, minor, details. The chosen attributes must fall within the normal ranges for a creature of that kind (these will be noted in the creature's description). As a rule of thumb, the assumed form's weight or dimensions can vary up or down by 10% unless a greater variation is allowed among typical specimens. The chosen weight and dimensions, however, cannot change the assumed form's size category.
(Although Williams co-wrote Dungeons & Dragons, Third Edition, the columns should nonetheless be read with a jaundiced eye; see here.) And, while they go unmentioned in this section, it's awfully convenient to extend this ruling to the ability change shape and the spells alter self and polymorph and similar abilities and spells.
Really, if this DM's advice above is rejected, and the column's advice is not taken or not extended, then—like this fine answer says—the DM closes these rules gaps. If the DM doesn't close these gaps before the PCs reach ECL 3 and start casting the alter self spell, the DM risks form-changing effects becoming an even more powerful strategy than it already is.
Keep in mind that this ruling does put a limit on disguises that both the PCs and their foes can achieve using using form-changing effects so that making disguises of some creatures is impossible without the creature while in the assumed form undergoing probably painful and damaging additions or subtractions. Players may initially balk at being unable to use a form-changing effect to impersonate, for example, General Croytsan who warp touch left with a snake tail instead of legs or Guildmaster Tiepiwsi who is covered in skin pockets (Dragon #359 117), but they'll eventually realize that receiving body modifications—perhaps even something as innocuous as a pierced ear—gives the entire setting an edge against the outrageous number of monsters that can disguise themselves (e.g. most metallic dragons, an ogre mage, a phasm, and the iconic doppelganger to name but a few). The players may not see this as ideal, but one hopes they see it as fair.
Does a creature's original form age while the creature's in an assumed form?
In this DM's campaigns, yes. The typical creature's original form is still subject to the passage of time, and the creature still suffers the normal effects of aging and dies upon reaching its maximum age (PH 109). The grim reaper still cuts down Archmage Reveneidem on his 110th birthday even if he's used a polymorph spell to become a bear. (Although this DM can imagine another DM ruling otherwise because, honestly, that story's so cool it kind of writes itself.)
Note: The bulk of the above does mean that a creature that somehow loses a limb and employs a form-changing effect to assume its own form assumes its own form with the missing limb now intact… yet also with merely average physical ability scores for a creature of its kind if appropriate (like with the polymorph spell). Honestly, this DM really would prefer the elegance of physical abilities scores remaining unchanged were a creature to employ a form-changing effect to assume its own form, but the issue then arises of assuming the form of any unique creature of its kind but that possesses arbitrarily high Strength, Dexterity, and Constitution scores using the justification that a creature of its kind must've had scores that high at some point. With this in mind, this DM rules against elegance in favor of balance and consistency.
1 Losing body parts is rare in Dungeons & Dragons 3.5, sometimes the result of adventuring (e.g. a petrified creature is damaged then its petrification cured as mentioned by the 6th-level Sor/Wiz spell flesh to stone [trans] (PH 232)) but more likely by DM fiat. In the latter case, if the loss seems arbitrary or malicious, this player supports a decision to leave that campaign.
2 Bleeding isn't usually a consequence of damage in 3.5. While the DM can narrate that buckets of blood gush from a wound, absent house rules or an effect that says so, that narration lacks mechanical import. This reader can't know what house rules are in play, but his totally blind assumption would be that an assumed form has no signs of injury so bleeding stops… in the assumed form. However, this reader can't even guess what'll happen when the creature resumes its original form!
3 Some form-changing effects can be outliers in that a creature that may be limited to one unique form (e.g. "[A]n aranea in its humanoid form always assumes the same appearance and traits" (MM 15)). This DM would rule that a haircut or the mundane tattoos of a unique assumed form like the aranea's or a lycanthrope's are kept whenever the creature assumes that form.
4 Some adjudication is still necessary here. For example, the stat block of the Monster Manual orc (203–4) does not possess average base ability scores (11, 11, 11, 10, 10, 10) but the nonelite array (13, 12, 11, 10, 9, 8).