It's perhaps best to check with Microsoft for software compatibility. Or wait for progress after release. You have twelve months from the July release date of W10, for a free upgrade.
Probably. I've been running all the Win10 previews on my Win8.1 without any problems, but others have had some problems. It just depends on your hardware and software, but Win 10 runs a compatibility check before it installs to tell you about any problems. BUT DO make sure you do a full system backup of your Win7, just in case you are one of the unlucky ones.
There have been enough reports here of the public releases LR having problems on Win10 that I would bet that is will not work reliably.
If you are using anything less than a "release candidate" for Win10, you are using beta software at best that should not be used for anything important, just testing purposes.
If you use Lightroom extensively and do a lot of work on it than i would recommend you to keep using it on windows 7 machine rather than installing it on os that's still in its beta stage.
However, if you just want to try, you can try it on your own risk, i can't assure you if its all functions will work as expected as the OS might have some loopholes/bugs that might affect the working of Lightroom.
Hope this helps with your query.