Tem vs Há?
Both are used meaning there to be. But ter is the most used.
he has a problem which he doesn't see ?
It is preferable to use "that" rather than "which" since the relative clause is essential to identify the "problem".
Both are correct, in fact.
*there is. Like if he´s driving with no gas and hasn´t checked the gage yet.. lol
There is and There's are the same. Also, Dosen't and Does not are the same.