Can one say one gets high on alcohol?

Yes, they can....in fact that’s not uncommon to say when someone is getting drunk.

"Now by this time I'm plenty high
You know when your mouth a-getting dry
You're plenty high
Looked down the bar I say to my bartender
I said look man, come down here, he got down there
So what you want this time?
I said look man, a-what time is it?
He said the clock on the wall say three o'clock
Last call for alcohol
So what you need?
One bourbon, one scotch, one beer”

-John Lee Hooker (as adapted by George Thorogood), “One Bourbon, One Scotch, One Beer"

It creates a dopamine release in the brain. So technically yes

Yes, how high do you want to go?

Technically alcohol is a drug so I don't see why not, but in comon usage here in UK we would tend to say tipsy (mildly drunk) or drunk (or any of a large number of other words (e.g. sloshed, inebriated, wasted, p*ssed, f*cked, w*nkered) instead which is more specfic.

One can say whatever they want

I don't know, i don't drink

One can if one wants 😂

Of course. Same process.

I usually show myself up then fall asleep.