Do some people actually call it "eyeglasses" in english?
eyeglasses is correct, but like telephone, shortened to phone, most people shorten eyeglasses to glasses.
Yes, but mostly in TV commercials.
I think that's just there to clarify that it doesn't mean the vessel "glass".
Wouldn't it be "por" miajn okulvitrojn?
No, because "serĉi" means "to look for". Try thinking of it as "to seek".