First the real weapons...
Any spell that says that it creates an item, creates an item. That the item is impermanent makes no difference in most cases. So you can cast a spell on an item made via minor creation, such as keen edge on a wooden spear.
The rainbow spell (Dr 321, p68) says:
A rainbow-hued longbow appears in your hand, along with a full quiver of arrows fletched in a variety of colors. The longbow is treated in all ways as a +1 longbow...
So any spell that can affect a +1 longbow will also affect the effect of the rainbow spell.
The arrows are not explicitly called out as being treated as arrows in all ways, but they are listed as being made of a variety of materials, so they should be what they say that they are: +1 magical arrows of [something] bane, made of [some material]. Any spell or effect that can affect a magic weapon made of whatever the arrow is made of (adamantium, cold iron, etc.) can affect the arrows created by the spell.
Regarding ever armed (Dr 335, p75), it says:
...a well-balanced +1 rapier and a brightly colored dueling cloak [...] appear in your hands.
No other information given, so these are what they say they are: a +1 rapier and a dueling cloak. They are eligible for any spell that any other item of the type is eligible for.
Other spells may be less explicit, but if it says that it creates a weapon, it does so, and that item can be targeted by spells as normal.
And now for something completely different...
Other spells don't actually create a weapon, but a beam or force or whatever that's wielded as a weapon. Flame blade is a good example of this type of spell. The spell says:
A 3-foot-long, blazing beam of red-hot fire springs forth from your hand. You wield this bladelike beam as if it were a scimitar...Since the blade is immaterial, your Strength modifier does not apply to the damage...
This is not a sword or even an item, but a beam, and an immaterial one at that. It's not an object, but an immaterial force. This may not disqualify it from being affected by certain spells, but in the case of keen edge for example, the fact that the "blade-like beam" deals fire damage rather than piercing or slashing damage, as keen edge requires, prevents it from being affected by the spell.
Other than keen edge, both magic weapon and greater magic weapon require that the caster touch the weapon, and a flame blade is immaterial (not incorporeal), which is not defined, so the dictionary definition is used, thus it's untouchable.
For other spells, such as Darternae’s Sword (near the end of the Wizards Archived page that the question refers to), the question is harder to answer. That spell creates:
a shimmering, swordlike plane of energy, [which] plane of force acts as a +3 brilliant energy keen longsword. You or another creature wield the sword as if you were proficient with it.
This seems very much like it makes an object that anyone can touch or use as normal. Even though it creates a sword-like plane of 'force' (but no force descriptor...) not a sword, it is a weapon. So any spell that can target a weapon that fits the description in the spell can target the sword-like force. (Heat metal, for example wouldn't work, as the sword-like force is not made of metal)
If the spell effect created is listed as an item, treat it as such. If instead, it's simply wielded as a weapon, it's usually a weapon (corner cases can likely be found), and it's thus as eligible as any weapon it's treated as. If it lacks required specific qualities (slashing damage, touchability, specific composition, etc), then it's ineligible for that spell, but may yet be for others.