easiest or most easily

Teacher Please help

Whats correct? point out differences and mistaken grammar

Which position can most easily score 3 goals in one match?
Which position can score 3 goals in one match eaisest?

Which position can most quickly score 3 goals?
Which position can score 3 goals quickest?

What basis can the rulers most [easily] persuade the population to support their aims [easiest]?
The ruler can [most] easily persuade the population to support their aims [easiest] basis that it's the right thing to do.

He can most easily climb up with those shoes.
He can climb up easiest with those shoes.