What happens if I have a minion that occupies more than one site (e.g. Mountain Giant) and also carries Land Deed?
Land Deed only grants you control of the site that Land Deed occupies.
If I gain control of a site in the middle of my turn, does it produce mana immediately?
No. Sites produce mana at the start of your turn and when they enter the realm. Since the site with Land Deed was already in the realm, it doesn't produce mana merely because you took control of it.
What happens if I have a Land Deed on Rubble?
You control the Rubble and your will if the takes , but the still doesn't provide . i.e. own a hunk of worthless rock!