A bit confused on this one, so if my rifleman is already upgraded with Bar, does that mean if i transform them to rangers they keep the bar?

smash karts

and i noticed rifleman veteran 1st rank gives you sprint, if i took sprint, after i transform it to rangers, what will happen?

Yes, they will keep their bar or any gun their were equipped before and experience and all future rangers you train will have one BAR with the BAR upgrade. Bonus tip if you want double BAR rangers you will need to get a second BAR on your rifles before upgrading them to rangers.