Unknown zone- Friends or a date?

I decided to try an internet dating site and had a few meetings with guys, I don't consider first meeting a stranger a date. A blind date is different bc usually it's a friend setting it up so you have some comfort with that. Well, I talked to this guy for a few weeks in messages and he asked for my number, gave me a call and asked me if I wanted to meet up that week. We also found out we have the same daily commute and work in the same building. Basically, I could see him every day if we ended up on the same bus or ran into each other going to work. When we met up for coffee, during work hours- I thought it would be brief- maybe 15 minutes- it ended up being 45 minutes before I realized what time it was and told him I needed to get back to work but that I wished we could continue to talk. We walked back to our jobs and mentioned getting drinks the following week. He called me the next week to set up a time to get drinks and an appetizer. We text messaged a little that day and met up that night. He was on time, as usual, and we had a great time chatting. We got a few beers and shared an appetizer and had fun talking and asking each other questions. We were there for about two hours. I mentioned that I was not very busy at work the next day and he said he wasn't either, and I casually mentioned we should grab coffee. When the check came, I reached for my wallet, as I always do, but although I don't mind paying, I've never had to on a date or with guy friends. We ended up splitting the check. He didn't even offer to pick it up. When the check came we both continued talking and when I reached into my wallet said, "Are you paying with a card? I will too." When we left, he mentioned he had a great time and said 'So, tomorrow morning do you want to get coffee with me?" and I told him sure. He texted me after we left that night something funny about our conversation at the bar. The next morning we ended up on the same bus and talked into work and parted ways. At exactly 10, the time he said he'd text me, he shot me a text asking if I wanted to go for a walk to get coffee. We walked around and grabbed coffee for like a half hour- again talking and laughing and asking questions. Maybe it's bc I'm all about chivalry, I notice that he sometimes opens doors for me but usually doesn't. The whole paying thing made me think it wasn't a date or that he wasn't interested. However, he's always been the one to call or ask me to hang out and he's always followed up. I'm not sure what to think, I would think he's feeling me out to see what he thinks of me- or that he's not interested in dating me but wants to be friends. Do guys pursue friendships with women off internet dating sites?