1) can do, as long as the will is made in legal matter.

2) Yes, she can *with reason, we have lot of such case out there. So legality issue of the will is very important.

But personally advise this is not a good move, as will can be changed by him without your notice as well, to avoid any problem and troublesome in the future, I would suggest either one take up the house. (trust is one thing, but this is to prevent any unforseen circumstance arise)

Joint name in properties create lot of problem if

1. either person passed away without will, or will is challenged lead to asset freezing
2. The other person suddenly 'face off' and disagree to sign.

In joint name properties, if either one refuse to sign, the properties cannot be sold or transferred at all.