1 - You can redirect the turning action (which includes the command >UNSCREW) to unlocking with an instead rule:
Instead of turning the battery compartment:
say "(with the screwdriver)[command clarification break]";
try unlocking the battery compartment with the screwdriver.
Instead of turning the battery compartment when the player is not carrying the screwdriver:
say "You don't have a suitable tool."
Note the second rule that takes care of the situation where the player doesn't have the screwdriver.
2 - You can again write a rule:
Instead of unlocking the battery compartment with the screwdriver when the player is not carrying the radio:
say "It would be easier to do that while holding the radio."
(This could also be a check rule, depending on what other rules there are for the unlocking action.)
On the other hand from game design perspective it's better to implicitly have the game take the radio instead of forcing the player to do it.
Before unlocking the battery compartment with the screwdriver when the player is not carrying the radio:
say "(first taking the radio)[command clarification break]";
try taking the radio;
if the player is not carrying the radio, stop the action.
The "if the player is not carrying the radio" makes sure that the game doesn't continue with unlocking the battery compartment if taking the radio failed for some reason.