Don't worry about the gil transferring, it's not unusual at all for players to trade millions to each other, especially if you're friends/FC members. I'm sure SE do watch money transactions, but if you came into the money legitimately you have nothing to worry about.

But to answer your second question, with the current system, no you cannot transfer a personal house and they haven't mentioned anything about that changing either. To transfer a personal house from one person to another you would need to relinquish (demolish) the house/plot and then the other person would need to buy it again straight at the full price.