What determines if it's a hit with mines? Do you role the dice or is it pr determined damage?
Slave 1 still on order
Since your Slave is still on order you do not have the sheet to refer to, so I'll elaborate.
As dbmeboy said, technically it is not a "hit" since a hit can only occur during an attack by another ship. So damage suffered from a mine will not, for example, remove a Stealth Device.
Prox mines detonate when a movement template or a ship base at the end of movement overlaps the mine token (much like asteroid tokens). When this happens, the player rolls three attack dice, and suffers any [hit] and [critical hit] damage that is rolled. There is no evading.
In reference to the OP, the first ship that triggers the detonation will suffer the damage, no other ships are affected.