Can dead mains-to-12V lighting transformers safely be left permanently connected to the main supply?
As to Q1 - since you don't know how or why they died, you have no idea whether they are still taking some power from the mains or not. 

If they've blown an internal fuse or something, then they might be effectively disconnected, so no problem.

If they've broken in some other way, you don't know if they are overheating or just sitting there passively doing nothing worse than slightly increasing your electric bill.

In theory in order to be rated for buried installation they SHOULD fail in some way that is 'safe'. On the other hand, even 'safe' stuff fails unsafely sometimes.

I personally would get them out of there, or at least cut a hole where they attach to the mains and cut &amp; cap the wires appropriately. 

Also, from a 'do it for the next guy' standpoint: powered, but useless transformers seem like an invitation for something to go horribly wrong for a future repair.