The white spot could be fungus or an injury. If you can get a clear picture that would help. Others here can recommend what type of treatment you can try or if you should take him to a vet. The big thing to watch out for over the next several days are signs of a respiratory infection. You can read more about it in the Health section on this website. That's probably one of the biggest killers of baby RES especially when they get all stressed out or were raised in terrible conditions like where you got him from.
And yes, baby turtles can drown if they get stuck underwater so you will need to do something to make sure he cant get stuck behind the filter.
Enjoy your new turtle quietly (handle as little as possible for the first week or so) and make sure the temperatures and basking area are good.





