It sounds like your landlord is having a hard time separating "her" house from "your" apartment, it can be hard to let that go when renting out part of your home.

As far as the mattress issue, is it a gas or electric hotwater heater and how close is the mattress to the heater? She could try arguing that the mattress is too close to the heater and causes a fire hazard, so that's an angle to be aware of.

If you feel she is violating your rights as far as her coming into the place unannounced try placing something small behind the door each time you leave so that when the door is opened it will get moved. Keep a written record of every you find someone has entered the apartment and if it really becomes an issue take her to court over it.
She has rights as your landlord but you also have rights as a tenant, you may have to fight for your rights if she is not complying with the law in that regard.