"Asked" a guy I like out for dinner. Not sure if he's gay?

So after realizing I might like guys, I've been trying to explore things further but have not been successful. A couple days ago, I went to this networking event where I met this guy, Elio. I was sitting behind him where I noticed he was looking at me. I looked at his direction but not at him, and I noticed he was sizing me up. At this point I thought he was cute, so I started talking to him. We talked about work and school. While we were talking, I noticed he was mimicking my body language, and his pupils were bigger--could be because it was kinda dark. After the event ended, I offered to walk him down to the lobby. When we were parting, I said that "I hope to see you again" & he responded "yea messaged me if you ever wanna chat". Later on I Facebook stalked him (dont judge ) and discovered that he liked the LGBTQ@Facebook page on Facebook. His sister looked gay, so I think maybe he could just be an ally (so not relevant. Sorry)? I later messaged him to see if he wanted to go out for food with me. He suggested that "it'd be nice" and "that sounds fun". He also asked what my availability was for the week. By the way, I suggested that we go to this really fancy and nice restaurant (I enjoy good food). And I plan to pick up the tab, not because I want to get with him (lol), but because I was the one who "asked" him out. Do you guys think that appropriate? Considering we did not officially say this was a date, and that his sexuality is up in the air. We later exchanged number, and he texted me to which I replied "Looking forward to seeing you again on Monday!". I did not receive a reply (lol). What should I do? At this point, I'd like a new friend. I, however, would also like something more with this guy. Should I keep hanging out with him? Or should I ask him if he's gay or bi? What should I do guys?