The answers are: it really depends.
Depends on the missile, for a start - the number you can fire depends on what way your ship is pointing vis. what way your missiles point, as well as the number of radar directors you have (if your missiles are beam riding for example). For most BOM-capable missiles all you need (as the name suggests) is an initial bearing on target and a distance at which the missile goes active.
There are missiles that can have target updates in flight for extreme range engagements where the targets may have time to get out of dodge.
Replenishment again depends heavily on the missile. Most of the big Russian ones are simply too big to do at sea. Those that can be reloaded take a long time to reload.