[NJMarine]

Pool pumps normal feel hot to the touch.
Pool pumps only have to run 6-8 hours to turnover(filter) all the water in the pool. If you do not have a timer on it, it might worth doing.

 

[NJMarine]

If this is the original pump than it shouuld be the correct one. If not than maybe someone installed a larger motor to get more capacity.
That may sound good but it will not work since the pool piping is designed for a certain flow rate. The filter, piping and pump are all designed to get all the water filtered in a 6-8 hour span.
Most pool motors do feel hot to the touch.

 

[NJMarine]

A inline chlorinater does not make aa impact on water flow