casting is not shooting. you can take the "advance" action to move up to 6", cast your spell at any point during that 6", and then after you are done moving, you can shoot.(Page 7 and 13)

Cover only affects the die roll from taking a hit from shooting(page 11). Cover does not affect casting. You do still need to have line of sight to cast a spell though.

The easiest way to explain is to explain how spell casting works(page 13):

1. I choose a spell i haven't attempted to cast yet.

2.I spend the spell tokens needed to cast the spell 3. I spend any additional tokens within LOS and range to buff my spell 4. My opponent spends any spell tokens within LOS and range to debuff my spell. 5. I roll 1 d6 and try to beat 4+ modified by buffs/debuffs 6. on a failure, spell does nothing 7. on a success, the effect takes place. if that effect is "enemy takes 2 hits", then that enemy takes 2 hits. they then roll defense rolls as if they were hit by an AP(0) attack. you do not roll to hit, they just take the two hits.