Using
$$F\_\text{magnetic} = (BIL)\_\text{wire} = (BQv)\_\text{particle}$$
we can say $F\propto v$ as $B$ and $Q$ are presumably constant.

Is the magnetic force proportional the radius, or distance, apart like in electric and gravitational fields?

Logically it makes sense; however, I've seen no proof of this.

Using this proportionality do we then say as the distance between the magnet and charged particle changes, so does the velocity of the charged particle; and as $I = Anev \rightarrow I \propto v$, the current subsequently goes up.