Pool heater for AG 15 x 33 oval

We just had a couple of questions. We live in Massachusetts and thinking about a heater. What would be involved with installing one

Could we use the same circuit as the filter itself for electricity

We leave for 5-6 days at a time in the summer, would we still leave it running when we are gone?
And if we did not leave it running, how long would it take to heat the pool back up, to lets say low 80s

And finally what is the pros and cons?

Will the monthly cost be a lot?