There is no 24 hour delay. You can stake as soon as you have enough coinage (1 Hour) But it will likely happen less often depending on your coinage and the network stake weight. The longer you wait the higher the reward will be. p to 5 days when you no longer acquire any more coinage

As far as I know 125k coins are required.

The keys are not addresses and will not unlock any coins. They just enable the stake rate for any address in the wallet. Which is now 100% for all the prime activation keys