The second one is like this :

The centripetal force created due to the circular path of the charge has to be equal to the magnetic force.

Equating the two;

mv*2/r=Bqvsin30

hence;

r=mv/2Bq

Clear the basic definition of current.

Current is the amount of flow of any entity through a cross-section in per unit time. Depending what the entity is, current can be - heat current, air current, charge current etc.

So here in case of electrodynamics-

 The charge which is circulating has the magnitude 'q'.

  As the path is a circle of radius 'r'. The total distance is 2TTr. The rate of flow of charge is 'v'.

We can conclude that the amount of charge flowing through a particular corss-section in a circle is

q*v/2TTr.

Or you can say that since i=q/t and t=2TTr/v. But the above method will aid you in arriving to the result in any situation.