Verified answer

Yes

unless you make the dogs sit before you die.

Yes, well it depends what difficulty you are playing on. If you are playing on hardcore your world will be deleted when you die but if you are playing on peaceful-hard and you die, as long as your pets dont die they will be back where you respawn then you will just lead them to your house.

Your pets teleport to you when you are too far away, so yes they should teleport back to you, if they don't then your game is broken, so yes your pets will TP back to you.