This is interesting, since I've heard differently. My teacher actually explicitly said that this is a north-south divide, where in the south of France the liason is used, whilst in the north it normally is not.
I'd be interested in hearing if any other natives have opinions on this? My teacher could be wrong of course, or just speaks with some specific regional accent, but I'd like to find out.
I'm pretty sure either "....est de/à moi" are acceptable for expressing possessio, but as Progressor says, "à moi" is somewhat more typical/colloquial. It might become a little more complex when talking about a something like a letter which is given and received. "Cette lettre est la mienne" might be the best option to unambiguously express possession.