In the end of House S08E05, House shows to his team that there is now a big remotely-controlled door between his office and Wilson's. What's the purpose of this door since it's not part of any other episode? How could he have made it without Wilson noticing?
This was mostly used as a throwaway gag. There is no future significance to the garage door. It was just to mess with Wilson and probably the ducklings as well.
Keep in mind that office walls tend not to be load bearing walls, and can be moved or replaced with relative ease (so offices can e.g. be resized).
The numbers are never made clear to us, but House had secured more than enough budget to jumpstart a new diagnistics department. If a couple of thousands had been left over, he would be able to pay for the prank. He has also never shown any apprehension to pay for things out of his own pocket when he wants something.