1- Recuva can attempt to recover the Directory structure, it may or may not be sucessful.
2- Recuva can recover all file types, including system files.
3- NEVER TRY TO RECOVER TO THE SAME DRIVE. ALWAYS RECOVER FILES TO A DIFFERENT DRIVE.
If you try to recover files back to the drive they have been lost from then you will almost certainly be overwriting the files that you are trying to recover - so will no longer be able to recover them.
Do not write anything to the drive that you want to recover from at all. The only thing you should be doing with that drive is recovering what files you can from it, once you have done that then you can start using it normally again.
If it is your main computer drive then stop using that computer, take the drive out, and do the recovery using a different computer.
If you do not have any spare drives to hand then you will need to buy, or borrow, a drive large enough to hold the recovered files.
4- Recovering files from a reformatted drive can be done, but it needs to be done in a particular way. (TBH I’ve never tried it with a drive that has been reformatted twice, but it should still be possible).
For how to recover files from a reformatted drive read this, and I suggest that you watch the video that is linked there too: