Confused...?? (Spoilers)

For the first question, yes, Yi Chan could talk. I think him using sign language was his preference. As far as I know while people with acquired deafness can still talk unless they also acquired muteness, pronunciation becomes more challenging and it's hard for them to control their speaking volume, so that might be the reason. Or maybe he had another reason too, who knows. About the actor's portrayal though, I can't judge it since I haven't heard any deaf people talk.

For the second question, yes, I think Yi Chan figured out that his son was the same person as his friend.

For the third and fourth question, I also hoped they would give us more insight about them too, especially about Yi Chan and Cheong Ah.

@Adri and @LunaticLady 

I think they did go to the same university abroad because on the brochure when Eun Gyeol looks up his dad you can see Yi chan's credentials and the same university as the one Chung Ah went to was listed. Since they specified it was a college for deaf people and that Chung Ah's dad would also fund Yi Chan, I assume this is how he managed to get the education he could not have originally and how he stayed with Chung Ah.

 For their house it's because Chung Ah stayed with her family, contrary to the original timeline, which means the house, estate and wealth that she did not inherit originally was passed on to her after Eun Gyeol's time slip.

I too want to know what happened to Eun Yuh and her mom. I assume things were better because she would have kept a relationship with her biological father and put less pressure on her daughter tho !