Hello MegaMike & welcome
You are aware of the age-gap concerns, so I won't go into them, except to say that teenagers change quite a bit over time ~ their interests, who they find attractive, etc, etc. You and she, if you get together, may not develop in parallel. You may not want the same things, after a while.
You seem to have started off well with this girl ~ especially as you managed to walk and chat for 45 minutes, almost as soon as you met. Just be yourself.
Letting her know that you are homophobic, when she has a gay cousin, may not go down well.
Being homophobic, whatever the reason, is not a good thing.
And no-one on here lets conversation fall into the gutter, unless they wish to be banned. I see no reason to even mention such a suggestion.
Asking for advice on any concern is a sensible thing to do ~ so well done on that ~ but, if I were this girl, I would not be too happy about you discussing & describing your meeting & worries on a public forum ~ not unless you did it anonymously ~ which you haven't, since there are two very recognisable photos posted.
Good luck
