Legal Question in Real Estate Law in California

I'm assuming by "own a house together" that you are both shown on title as co-owners, e.g., tenants in common or joint tenants. Further, I'm assuming there are no contracts between the two of you that would have the purpose or effect of modifying the usual rights of co-ownership, and that the house is, as you say, vacant.

If so, each of you is entitled to possession of the entire property at all times. This basically means you have the right to move back in, and may do so at your pleasure. Your ex-partner has the same right.

Now, here's where things get a little muddy. Once the house is occupied by one of you, the other's right to possession/occupancy is still present, but cannot be exercised in a way that might result in a disturbance of the peace, i.e., against the will of the co-owner who is already in possession -- not because the out-of-possession owner has a lesser right, but because the law doesn't like self-help exercise of rights when someone might get hurt -- thus an out-of-possession co-owner has to go to court and get an order restoring co-possession.

This pretty much means your answers are NO, he cannot block you from living there, and NO, he or his representative cannot come into the house while you live there if you have locked him/them out are refuse him/ entry -- such a lockout technically violates his rights but he cannot properly exercise those rights without a judge's order restoring him to co-possession.

Please note that this is an abstract discussion of the law, and not a prediction of how some particular human being is going to behave. You may want to consider getting a restraining order. You may also want to consider unwinding this co-ownership situation through negotiations or a partition lawsuit when the time is ripe, market-wise and otherwise.