need help with all of my turtles

[Smilts]

First I have a red eared slider recently baught for my 6 year old. he seems to be spending lots of time out of the water,
I have him in about 4 and 1/2 inchs of water with a log to get completely out of the water and a rock he can rest on mostly out of the water. he pretty much gets on the log out of the water and stays there there. Also he seems to maybe have a RI as he had what looks like bugers on his nose when I got home from work, and he's very inactive.



Now for my other two turtles these guys I dont know what they are a friend of mine was mowing his lawn and very on accident ran over a turtle when he went to look at what he hit there was two turtles of diff sizes but same breed rite near where it happened. Well I keep snakes but he figured he would give them to me.
As for that they are small one about 2 inchs round the other about 1 inch round. unlike my slider they have raised shells, my dad called them box turtles around here you see them on the side of the road all the time. well they dont seem to want to eat though they may be. very inactive also wich I figured to be shock so they are in a back room beng left alone other htan water and food. The water they drink or at least appear to im worried about the none eating thing though

Any Advice at all on either or both problems would be great thnx!