I'll do my best to answer your points.
1. I'm afraid he does still have the right to access the marital home. However, at some point fairly soon, it's reasonable to ask for notice of him coming to the property if he has set up home somewhere else. Legally there may not be a requirement to do this, but reasonably he should be prepared to do so.
2. You can ask that he waits for 2 years to divorce. Though if you want to be able to move on and from what I can tell you do, then I would advise to go ahead with the divorce sooner rather than later.
3. You have joint obligations still, and if he was the main earner, once divorce is applied for you may be able to claim spousal maintenance from him pending the outcome of the divorce. This is another reason to consider applying for or accepting a divorce petition sooner rather than later.
4. You should agree on the division of the joint possessions. If you cannot agree, then again, going through the divorce application will be an opportunity to do this in a more formal setting. Until then, you both equally own everything, and you cannot really stop him from taking things that he has just as much right to as you I'm afraid.
I'm sorry that there's no easy answer here, and that it will feel like there are no consequences for his actions. But the law doesn't punish someone's behaviour when a relationship breaks down, though it feels like it should.
I hope that this clarifies some points for you, if you do have further questions you can comeback to me, of course.