You do NOT still get the benefit if you take the item off.
Permanent Bonuses: Ability bonuses with a duration greater than 1 day actually increase the relevant ability score after 24 hours. Modify all skills and statistics related to that ability. This might cause you to gain skill points, hit points, and other bonuses. These bonuses should be noted separately in case they are removed.
That is what it means. After 24 hours it falls into the permanent bonus category but only as long as you wear it.
Skill(s) and Language(s). +6 INT headband should have 3 Skills and 3 Languages listed.
It's a hassle for the GM to provide those.
The bonuses have more to do with INT/WIS/CHA stats. As a temporary bonus, a Wizard for example doesn't get a bonus spell slot, via a higher temporary bonus to their INT. It's only after 24 hours that a caster gets that bonus slot. A lot of other abilities benefit character classes by enabling +x / day based on ability bonuses. If a character is still in their 'temporary' term of the bonuses, they can't get extra uses/day and the like.
But no, once you take off the item all bonuses are gone, and you have to re-warm-it-up from scratch.
Compare this to this FAQ:
Temporary ability bonuses should apply to anything relating to that ability score, just as permanent ability score bonuses do. The section in the glossary was very tight on space and it was not possible to list every single ability score-related game effect that an ability score bones would affect.The purpose of the temporary ability score ruling is to make it so you don't have to rebuild your character every time you get a bull's strength or similar spell; it just summarizes the most common game effects relative to that ability score.
For example, most of the time when you get bull's strength, you're using it for combat, so the glossary mentions Strength-based skill checks, melee attack rolls, Strength-based weapon damage rolls, CMB, and CMD. It doesn't call out melee attack rolls that use Dex instead of Str (such as when using Weapon Finesse) or situations where your applied Str bonus should be halved or multiplied (such as whith off-hand or two-handed weapons). You're usually not using the spell for a 1 min./level increase in your carrying capacity, so that isn't mentioned there, but the bonus should still apply to that, as well as to Strength checks to break down doors.
Think of it in the same way that a simple template has "quick rules" and "rebuild rules;" they're supposed to create monsters which are roughly equivalent in terms of stats, but the quick rules are a short cut that misses some details compared to using the rebuild rules. Likewise, the temporary ability score rule is intended as a short cut to speed up gameplay, not as the most precise way of applying the bonus.
A temporary ability score bonus should affect all of the same stats and rolls that a permanent ability score bonus does.
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Not sure if I could make myself allow for more skill points.
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No. The skill associated with the magic item represents the "retroactive" skill ranks you'd get from the item increasing your Intelligence. You don't get the item's built-in skill ranks and another set to assign however you want.