Is this a date?

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Alright tomorrow I am going to dinner with some girl I met. I am not sure if its a date or if she is a lesbian or something. Let me explain:

>Just moved to a new city for work.
>Go out last Friday by myself to get drunk so I can forget about my shitty life.
>Walk around not sure where the fuck I am.
>End up in a place that is either a club or bar I wasn't sure.
>Get drink at bar.
>Look behind and me and realize I somehow ended up in some gay bar/club
>Dudes literally giving each other blowjobs.
>Start feeling really uncomfortable.
>Never looked at the crowd before getting the drink because I just focused on the bar and my drink.
>Accidentally lock eyes with some girl who smiles and quickly turn away and look at my drink.
>Trying to finish my drink when she ends up coming over to the bar and taps me on shoulder.
>Can't really remember what was said other than they took my phone from my hand and called theirs with it.
>Only thing I remember them saying is I look like I don't belong in that place and after they called their phone using mine they said they would text me later.
>Chick leaves with two gay guys.
>Finish drink and run out of the place and end up just buying a bunch of alcohol at a convenience store.
>Go home and drink it until I pass out.
>Wake up thinking I imagined the whole thing until I look at my phone later seeing that I got text messages.
>Girl convinced me today to get food tomorrow.
>Apparently they live with their parents and are expecting me to pick them up in my car.

Does this sound like a date? How can I ask if they are lesbian who just sees me as a friend since I literally met them in a gay bar? Any subtle ways to ask if they are lesbian? I have never been on a date either so I am confused as fuck how to dress for this situation. I really need some advice on how to act.