My new boyfriend - can I really trust him?

I met a guy at a bar. He approached me and we chatted for a while and then he asked me to come to his place to continue our chat. I usually don't go with anyone but this time I decided to go and see if he really just wants to talk as he claimed. Well it turned out he just wanted to have sex, as he was quite pushing for it, though we had interesting conversations aswell. I didn't have sex with him that night.

I don't know if this is relevant but he asked me if I could date a man who has a child. Turned out he had. I didn't care. Next day he said he wants to meet again. We had fun, he still tried to have sex but not as much as the night before. After this he sent me some messages which really made him look like a player - so I playfully answered telling him what he should text instead so he wouldn't look like an obvious player. He laughed and promised to remember my advices and told me he was actually a player and made fun of that.

I thought I wouldn't be in contact with him but after a few days we ended up playing an online game together and then again chatting. He wanted to meet again. I didn't think anything serious about it but I decided to see what happens. We had fun together. He seemed to have changed, respected my opinion of not having sex unless in relationship. And about that player thing, he said "I'm not a player but if you say so then maybe I am, I can't make you believe me". (I also asked him if he was a gay and he admitted that too.. don't know what to think about this).
We had many dates, both at weeks and at weekends. The dates were quite interesting - we mostly were outside, walked in parks, talked a lot, played games, went to bar etc. Sometimes I were at his house.

After a few weeks he started to talk about his feelings and getting serious. I started to have feelings aswell. Now we have been in a relationship for two weeks and I still don't know what to think. I just want to be sure I can trust him. He has introduced me to his friends as his girlfriend, and he also has met one member of my family and two of my friends. However neither of us don't want to introduce eachother to our parents yet.

Anyways, there are few things that has raised my suspicion. One day I saw he had changed my name in his phone to a guy's name by taking off few letters. I asked him why would he do that and he told me he had misspelled it the first time we met. I managed to prove he was lying. He seemed confused and then "remembered" changing my name for our inside joke (which I actually would have understood if only he had told me that the first time I asked..). I let it be but still wonder if he really didn't remember or was he just lying. I don't know if I'm just thinking too much.
Then there are two things that I don't know if I should be suspicious of? He says his sister lives in his apartement at weeks. He can't introduce me to his sister because "she will tell my parents". So I haven't met his sister whose clothes and stuff are always displayed in his home. He still doesn't seem concerned if I forget something in his apartement or anything. Idk. We are friends in facebook. I easily found his ex (who has a child with him) from his friend list. She has a picture of her, him and their baby in her profile pic. The pic is almost a year old but it's still a bit weird...

All in all he seems pretty honest tho. We see eachother at least two times a week. Always in the evenings or in the weekends. He always comes from almost an hour driving distance just to hang out with me for a few hours. He has also said to me that if our relationship doesn't work he at least wants to stay as a friend because he likes me so much he doesn't want to lose me. We still haven't had sex. He says it's no problem for him to wait. Is there still a possibility that he is just playing and making this big an effort just to get finally laid? Is there a possibility he has other woman? What should I think or do? Can you tell by this what are his intentions? Please tell me what do you think about this