The stats received imply quite a lot:
Average intelligence -- The polymorphed creature shouldn't be perceived as a simpleton or ignorant. No penalty to knowledge checks implies an average level of knowledge.
Average wisdom -- Should appear to operate on basic common sense (knows when to come in from the rain). No penalty to sense motive checks implies not naive.
Average charisma -- Interacts normally with others. No penalty on diplomacy checks implies that it knows the niceties of local interaction, and generally doesn't come across as creepy.
So when you polymorph the hair into an elf, you get an elf. They might be missing very specific knowledge (like the best place to grab a coffee in the major elven town), but they are otherwise indistinguishable from another perfectly average elf: They know what gods to worship, how to interact with each other, how to care for themselves in their native environment, etc.
Individually, your elves are fine. Average, but fine. Where you're going to run into problems is as a society. Your elves are going to be completely lacking in specialists:
No great leaders to run the society.
No great architects and builders to build and maintain their cites/infrastructure.
No great generals to protect them.
No great scholars to remember the details of their history.
No great priests to maintain their relationship to their gods (beyond the basics of worships the average elf knows).
How big of a problem this is depends on what your PCs do to prop up the new society, and how you handle the advancement of NPCs in non-adventuring classes.
Note that this assumes an elvish mono-culture, as is typical of D&D. If there are many elvish cultures in your world, the PCs should either pick one or the DM should select one at random (or pick the most dominant one).
What is your Intelligence score?
I think we can look at this like a program. We are doing so ONLY as a method of thinking about this problem, NOT because this is how the game works. Below I will describe an update loop and the like, but the game does not run on such a thing. This is based on the phrasing.
The headband is not a one time occurrence, it is a continuous loop. It uses the word while.
Your Intelligence score is 19 while you wear this headband.
If we look at it like a program, we're setting the Intelligence to be 19 every "update". Or rather, every moment in time. Is the headband on? if yes, your intelligence is 19.
Feeblemind is a one time effect, meaning one time and one time only, we're setting the creatures Intelligence and Charisma to be 1. It has a duration of "Instantaneous", which implies that the effect is not contingent on the duration of the spell -- It is not 1 "while this spell is active", like the way the headband sets your intelligence to 19 "while you wear this headband". It is just set to 1. Without interference, your intelligence will stay 1.
When the headband is considered, your intelligence becomes 19. You can wear the headband because that is not the same as activating it, which the spell prohibits. If the headband's wording used "when" or "after" you put the headband on, we could conclude that Feeblemind would win out, as it was the latest effect on your intelligence. But because it uses "while", we treat it as a continuous effect.
Can I communicate, understand language, cast spells, and activate magic items?
Because of the wording of the spell, you still cannot speak, cast spells, or anything like that. The spell does not give a condition on the secondary effects' end, other than the spells that can dispell it, so we must conclude that the effects are ongoing as part of the spell itself, not because of the mental scores of the target. It is not because of the intelligence score that you cannot do those things, they are separate from each other.
Furthermore, Intelligence is not described as being important for language. Page 12 of the PHB states that Intelligence is a measure of mental acuity, information recall, and analytical skill. On page 17 of the PHB, you know certain languages "by virtue of your race". You also acquire some from your background. In the DMG page 278 for the language of a created monster, there are no ability score requirements for language. There are some spells that don't work on creatures of poor Intelligence, some of them regarding communication, but other than that there is no other requirement to be able to understand or speak a language. If you want more reasoning, there is a very good answer for a similar question I posed regarding Intelligence and Language
We must treat the inability to understand languages, activate magic items, etc etc, as an effect that the spell is having on your character, not as an effect the low intelligence is having on him/her. Call it "brain fart on steroids" if you want. You're smart, but you just can't do certain things. Your Intelligence is 19, you're very good at recalling information and can make good saving throws, but you cannot cast spells, activate magic items, understand language, or communicate in any intelligible way.
Best Answer
Yes
Assuming you are talking about the polymorph spell (other spells may vary but most will actually have the same effect).
The spell states:
So if the target is polymorphed into something with higher mental ability scores then yes - they may end up smarter, wiser and/or more charismatic! At least until polymorph ends.
Note:
Some argue that this would not work because Feeblemind, being a higher-level spell, would override a standard Polymorph.
However, as Mindwin points out in his own answer, the rules about overlapping spell durations (which states only the most potent effect applies) would not apply here because Feeblemind is an instantaneous spell. Its effects may last a long time, but the actual spell itself is instant. Hence even a standard level casting of polymorph would temporarily override those effects.