How should I encourage him to confess his feelings towards me?

[Rita]

Recently, this guy from my university asked me out to lunch and we ended up going to the mall afterwards as well. I was out with him for around 5 hours and our conversation never went dry. He subtly told me that he's single right now by saying that his friends asked him to ski with them but he didn't go because they were all couples. He also kept on asking me who else I know in our program (at university) and asked me if I knew this guy and that guy. When we were at the mall, I said I have to go buy a drink because I was really thirsty and he offered me his water (he already drank half of it before) and he later finished the rest of it while we were walking. I was telling him about my phobias and he also told me about his and said that he doesn't usually tell people about it. He also opened almost every single door for me and asked me to walk first whenever we were at a narrow path and were unable to walk side by side. He also told me about one of his favorite songs, which was a song called "One and Only" in Mandarin. When we were sitting and talking at the bench in the mall, he slowly moved his foot towards mine such that our feet were touching, but I moved my foot away (not too far away) after a few seconds and he didn't try to do it again.

However, we didn't hold hands or had any other form of physical contact yet except for the accidental touching of our hands when we were looking at the price tags of clothes.

Do you guys think that he likes me? What should I do so that he would confess his feelings towards me if he does like me? Is it alright for me to tell him I miss him a day after our date/outing?

By the way, we always talk to each other when we see each other at school.