Sure you can. You can take title together as tenants in common or joint tenants. Joint Tenancy ensures that the full interest of the property passes to the survivor of the two, while Tenancy in Common deals with split interests, so to speak. Upon your death, your half would be split amongst your heirs, while the other tenant retains their half.
You will most likely be filing a quit claim deed from the current owner to the new co-owners. As Gary pointed out, make sure you take ownership correctly. Joint Tenancy with Rights of Survivorship is how married couples generally take ownership so that if one passes, the home transfers to the other. You do not have to be married to take title that way though. A settlement attorney will probably do it for you for about $250 and that includes filing the new deed. You may also want to talk to your accountant to make sure there are no tax consequence to consider.
Yes. But talk to a real estate or settlement attorney to make sure the form of ownership meets your objective. In the event of your demise, should the other person on the deed become the sole owner or should your portion it go to your estate or your heirs? It is probably worth the money to make sure you get it right.