Glasses - countable or uncountable noun?

Words such as glasses, pants, trousers, or scissors/shears are plural only; the technical term is the Latin pluralia tantum, sg. plurale tantum. The word in the sense of eyeglasses is not countable: if you break a pair in half, you don’t get a right and left *eyeglass, only a useless half a pair of glasses in each hand and a trip to the optometrist. You have to say my two pair(s) of sunglasses just as you have to say three pieces of luggage.

Words like "glasses" (in the sense "eyeglasses", not "drinking glasses") are kind of unusual. I don't know how useful it is to just call it "countable" or "uncountable", although if I had to choose I would say "uncountable".

You’re asking about several different things here.

These glasses (referring to one pair of glasses) are my favourite!

This is acceptable. "Glasses" triggers plural agreement on other words in the noun phrase. It also triggers plural agreement on a verb that has a noun phrase headed by "glasses" as its subject.

I have quite a few glasses in my drawer, however, my favourite ones are red, dark blue and black.
I have lots of glasses in my drawer.

These aren’t acceptable for me. The first seems worse than the second for some reason. Maybe there are some speakers that would accept one or both, but in general, "quite a few glasses" and "lots of glasses" would be understood as referring to drinking glasses.

I have lots of pairs of glasses.

This is acceptable.

You can say either “What is this?” or “What are these?”; I don’t think it makes much difference. The question doesn't contain the word "glasses", so I don't think the plural form is mandatory, but it seems possible.

Sometimes a noun that is plural for some speakers can be used as a singular by others. See this post by a speaker who says “a scissors”: Is "pair of scissors" more correct than "scissors"? (Some nouns have even started as singular and come to be used as plural, like forceps, from a Latin singular form.)

But I’ve never heard “a glasses”.