First off, hi and
Here's my take on your questions:
1) You need to have at least 3 hours of solid sleep before taking your temp. You must take it before moving, talking, getting up, etc.
2) You can start whenever, but know that if you start mid-cycle you may not catch O--although, since you just got your Mirena out, you may not O right away.
3) You can O....and go a looong time without a period....but if you mean have the Mirena and O, it's very very unlikely. First, the Mirena has hormones in it so that you don't ovulate, and then the IUD is there to prevent an egg from implanting. When you O though, you will eventually have a period. Hope that makes sense.
Good luck!