1) In terms of Mobility, I believe pug --> monk requires more precise movement because of specific flanking and behind attacks. ( I noticed flank doesn't count when you're behind, only on the sides. So if pug/monk has flank and another skill for behind, boss fights will be alot of dancing to be optimal in damage output. )

Visual mobility, Lancer --> Dragoon has the flashy things, like jump. Jump offscreen gogo. Of course you have flank attacks for lancer as well.

2) Lancer/Dragoon ( or LNC/DRG ) Will end up having more Burst. But I think the general consensus is a well played pug/monk ( PUG/MNK ) will have higher consistant damage.

3) I think pug/mnk has faster gcd times cause of greased lightn.

4) You have access to sprint in both classes. Just pop it and run away. If you mean while in dungeons for aoe etc, not sure. Haven't gotten that far yet, but I do believe DRG ends up getting a disengage jump. Don't know about MNK.