Hey there! Sorry you haven't gotten a response yet. I hope I can be of some help.

Honestly I think it's fine to ask him about spending more time together and seeing where things go. Admitting you have feelings for someone, especially without knowing whether they reciprocate those feelings, can be a big, scary, step, so it might be a bit easier to just try and see if y'all can hang out some more one-on-one. Hanging out outside of work, especially when your first experience seemed to go so well, is a positive sign, and while it doesn't necessarily means he has romantic feelings for you, it opens the door to the possibility of a relationship beyond that of "coworker," even if it's just as friends.

As for why he hasn't met up with this girl he likes, or whether her not he is being catfished, I can't possibly comment. While I firmly believe that "talking to" someone from a dating site does not mean you are committed to them or in a relationship with them by any means, it does sound like he does have some interest in this person at this point, and until you know him better you might also want to carefully weigh the pros and cons of telling him outright how you feel. In the end, though, you have the most insight into the situation. If you feel comfortable just sharing your feelings, there is nothing wrong with that, so long as you keep in mind and perhaps cope ahead for the possibility of him not feeling the same way you do. But if you feel like you want to tell him if/when you are leaving that position and you think you can handle it if he says no, it might not be a bad idea to just say something, if that's what you feel is in your heart.