Do airline pilots get to go home often to see their family and have a break from flying planes. If so, how many days?
All in the contract, routes, and choices of the pilot within that contract. Some fly trips of up to two weeks, others are back home every night if they have a home near their base airport and work regional. Some choose to take all available work offered while others stay near the minimum. 

Labor law limits total flying time per day and per week depending on crew size and time of the day.