By the most current rules, you lose Composite Plating when you alter self.
The most recent version of the rules on Transmutation spells is the Rules Compendium (2007), which includes the Polymorph subschool introduced in Player's Handbook II (2006), of which alter self is retroactively a member.
With the exception that a spell's text takes priority over the subschool definition, the following rule is true of alter self:
In all other ways, the target's normal game statistics are effectively replaced by those of the new form. The target loses all the special abilities it had in its normal form, including its class features, even if the new form would be able to use these class features.
The result is that alter self now explicitly causes you to lose all special abilities, except for those which either alter self or the Polymorph subschool definition explicitly state that you retain.
What type of ability is Composite Plating?
Depending on your source, the warforged's Composite Plating ability is either a Natural Ability, or an Extraordinary Ability.
In the Eberron Campaign Setting (2003) and Races of Eberron (2006), Composite Plating is not defined as Ex, Su or Sp. According to the Player's Handbook, p.180, all abilities which are not defined as Ex, Su or Sp are Natural Abilities:
Natural Abilities: This category includes abilities a creature has because of its physical nature, such as a bird's ability to fly. Natural abilities are those not otherwise designated as extraordinary, supernatural, or spell-like.
In Monster Manual III (2004), Composite Plating is defined as an Extraordinary special quality. The DMG p.289 and MM p.6 both concur that all special abilities are either Ex, Su or Sp. However, MM III updates the monster rules that a special ability is merely usually categorized as Ex, Sp or Su, not always. Nevertheless, the particular warforged monster race rules in MMIII define Composite Plating as Ex.
Composite Plating is therefore a Natural Ability, unless you intentionally choose the version of the race appearing in the warforged monster entry in Monster Manual III, in which case it is Extraordinary.
Can a warforged retain Composite Plating if it is a Natural Ability?
The spell description of alter self does not include Composite Plating, armor bonuses, or natural abilities in general in its list of things which you retain.
Can a warforged retain Composite Plating if it is an Extraordinary Ability?
You do not retain it because your Composite Plating ability was not derived from class levels:
You keep all extraordinary special attacks and qualities derived from class levels, but you lose any from your normal form that are not derived from class levels.
What about Adamantine Body?
Like most feats, Adamantine Body feat is not listed as Ex, Su or Sp, and is therefore a Natural Ability. You retain your class and level, and therefore arguably retain all the benefits of level, including feats. The FAQ, p.7, even argues that you technically don't need Composite Plating to take feats like Adamantine Body; you just need to be a warforged.
However, the Polymorph subschool asserts that:
In all other ways, the target's normal game statistics are effectively replaced by those of the assumed form.
For the duration of an alter self spell, you are no longer a warforged. You therefore no longer meet the prerequisites for Adamantine Body, and as per PHB p.87 this means you can no longer use that feat. It would be particularly noodly to argue that you're still a warforged deep-down, but perhaps you can convince a DM to accept that argument.
Whenever you lose composite plating, you're also going to lose any modifications to it. That includes magical enhancement bonuses and other magical properties. It's effectively the same if you were wearing bracers of armor, absorbed them into your new form, and they stopped working. You can't logically benefit from an item you don't have.
You could get extra noodly and argue that your armor enhancement is a supernatural quality, but as per alter self these aren't retained if you lose the required body part (your composite plating). You could argue that your armor is a magic item, the rules for which are clear:
When the change occurs, your equipment, if any, either remains worn or held by the new form (if it is capable of wearing or holding the item), or melds into the new form and becomes nonfunctional.
Unfortunately, Composite Plating is a warforged-specific technology, and no other known creature in the books is "capable of wearing" it.
Armor augment crystals can only be placed into masterwork or magical items. This means your new form must be masterwork or magically enhanced, or you cannot use continue to benefit from it. You could, I imagine, simply transform into an animated suit of masterwork armor.