A unit always moves at the same rate as the slowest model, so when the unit moves, charges, flees or pursues, always use the lowest Movement characteristic and rules of the slowest troop type. Similarly, if the character is subject to any movement restrictions, then those restrictions apply to whole combined unit whilst the character remains part of it, and vice versa.
Characters can change position inside a unit as part of a normal move, as long as they end up in the front rank of the unit. It is also worth remembering that even if only the character moves the whole unit will count as moving that turn. Having a belligerent officer barge their way through the unit is not conducive to a good round of shooting!
If a unit containing one or more characters has had its Movement Allowance altered, this will affect a character leaving the unit, including if they try to charge out of it, but for that move only.