Will the size of a parachute affect the speed of falling object?

In logic, yes. There are a few things to consider though. I jump a 35 foot parachute and descend about the same velocity as a 21 foot low porosity fabric parachute. A more modern approach is the ram air canopy, effectively an airfoil and with 100 square feet, can control forward velocity as well as descent velocity, Ideally zero velocity when my weight touches the ground.
Another factor can be a parachute 'too large' to inflate properly reducing its efficiency.

Yes. I'd explain how and why, but I am assuming this is a homework assignment or for a final project, in which cases I am not allowed to give you answers as my job is/was a tutor

yes of course it would do to air resistance