1-3 of 3 Answers
Yes, the Wifi system will work in an RV motorhome.
Technically yes. If your home is less than 1000 square feet however, a whole home system is not necessary and a one-router AC solution is good enough. (Never buy N routers at this point, they are terrible)
As long as there is an internet connection coming into the mobile home, they absolutely would, but it's probably overkill for such a small space. Any good router using the 802.11AC wireless spec should work well for you.