Re; Knocking doors down. You can get a big brass or steel latch plate for your door. It replaces the little brass plate that comes with the door. You secure it to the door frame with sturdy 3+ inch screws. Then if someone tries to kick the door in the force is spread over a much wider area using screws that are much more securely attached to the wood than normal screws. That means they have to hit the door a lot harder to break the door open.

It won't stop someone breaking in if they really want to, but it'll prevent someone from kicking the door in in a couple of kicks. Probably one of the more effective security measures you can do that actually helps somewhat and has some actual value.

There are also all kinds of floor wedges. Some you just kick under the door. Others, you drill a hole in the floor and if you want to keep someone out you drop the wedge in so the door cannot open. They make it much more difficult to open the door without actually destroying it.

Re: the bat;

I would strongly encourage you to get some pepper spray as a first option. One of the nice things about pepper spray is that outside of some medical conditions it will not kill or seriously injure the other person. You don't have to threaten them with a weapon and hope they leave so you don't have to hurt them. You can just spray them down as soon as you see them. They'll recover on their own in an hour or two and be no worse for wear by tomorrow. And the way pepper spray works - it forces your eyes shut, it makes you snot everywhere, breathing will hurt like hell, your skin burns, it all means that fighting becomes effectively impossible for someone who has gotten a face full of it.

Those two key things; You won't kill them or even injure them, and they'll be totally unable to fight, make it a very good option for defending yourself. You also don't need to be physically strong or a good fighter to use it. You just point and hold the cap down until it's empty.