You're right - the first ("percent") doesn't work for me. It's likely that some would argue with me but for me, "percent" is only the number or a representation of a number. When speaking about a "portion" of a group (ie. the glasses wearers), the mathematical calculation arrives at a "percentage". It may be that 80 "percent" of the class wears glasses but that means that the "percentage" of the class that wears glasses is 80.
A conversation might go like this:
A: "Do you know that 80 percent of the class wears glasses?"
B: "Wow, that's a high percentage!"
What percent of students in class wears glasses?
Thanks, Dimcl."Theoretically", you can use the plural "percents" in the same manner that you would use "percentage" but this is very uncommon and might be considered incorrect because of its rarity. I would not, therefore, use it.
"How many percent" is incorrect. A "percent" or "percentage" is singular in this context so the plural doesn't work.