1999 Dodge Durango hard to start, stalls when lights on

Ny truck got a new water pump and fan belt last week. It started yesterday to not start. Changed the battery termials and the negative teriamal wire and negative ground wire Also cleaned terimals. Had "auto zone store" test the battery and alternatior, they said the battery was a little low (not much) and the alternatior was fine I THINK THAT THE NEW BELT IS NOT TIGHT ENOUGH AND IT IS NOT RECHARGING THE BATTARY< MAKING IT HARD TO START. IT WILL START WITH A BOOSTER PACK, BUT SOMETIMES IT TAKES A COUPLE OF TRYS. Also it stalled before (like just died out) when it put my headlights on, I had to keep my right foot on gas (reving it) and brake with left just to get home, when I turned off the headlights the problem went away and it stayed running. Also the battery gauge in the car returned to above half, with lights and radio on the car stalls and battery gauge drops down. The man who put the new belt and water pump in last week said that I might need a new "tensioner" (the bolt that tightens the belt. This is my question---
do you think its the battery or need a new tensioner so the belt is tigher so it charges the battery better
Please tell me what I should do?