In addition, our landlord aggressively INSISTS that such electricity consumption is normal.
They are not normal: he is very clearly lying to you and robbing you. I just happen to have my electricity bills for the last half year in front of me (one person living in a 50m flat but one who is often up late and not very good at cutting down energy use): they are for 169.28zl per two months. There is no way that your landlord thinks that 1000zl per quarter is normal in a flat which does not have electrical heating.
I strongly suggest that you ask to see original fakuras complete with the red bank form at the bottom. The amount you have to pay is in the box title "kwota". If those amounts are the same as he is asking for, you need to go with him to RWE (with a Polish speaker) and ask them to justify the amounts. If he refuses to show you originals or to go to RWE with you, write a list of the amounts you have paid and tell him that he must either refund those amounts or you will file formal notification of the suspicion that a crime has been committed (the crime being obtaining money through deception and/or false billing and/or forgery (use of falsified documents, i.e. the facsimiles), i.e. fraud). In addition to that, you will also file with the tax office a letter stating all the amounts which you have paid him since moving into his flat (I guarantee that he is not paying all the tax which he should on that money).
No matter what you do, you need to move and do it now: if he's happy to steal money from you and he's got a set of keys to your flat, why wouldn't he steal your property?