You get them at exactly midnight (of home terminal time, not necessarily local time). Say you start your day at 10:00 pm with only 2 hours left. You can work a full 14 and not even have a blip as as soon as the 2 hours are used you have 12 left to use.
You don't need to take a 10 to get those 12 hours back.
Yes wherever you stop to take your 10 you will have what's left of your 12 recap hrs, ( you have 12 at midnight, you continue to drive for 4 and take your 10, you will have 6 left)