Got a bad landlord?

Sorry, I don't speak gibberish

Assuming nothing important was mentioned in the parts of this that were incoherent, you should be fine.  I would talk to him before going to court, just to give him a chance to make this right.  But do it verbally, not in writing.

He obsiously can't hold you to a new lease that you never signed.  Its not really illegal to say its the lease but without your signature its just a piece of paper.  For the other stuff I suggest calling code enforcement.  These are things that have to be provided (for the most part) and I'll bet there are other things in the unit not up to code, as well.  Code enforcement will make him do these repairs and if he doesn't you will be able to move out but you do have to give him a chance to make the repairs, so call code enforcement first.

If he fixed those items then you have no case.

If they are not then you have to follow the legally required steps for your state before you can sue. Suing is the LAST step, NOT the 1st. The 1st legally required step in all states is to submit a WRITTEN work order request for those items to be fixed. It does not matter how many times you told him about them. The # of days he has to fix it & the remaining steps all vary by state which you failed to include.

No any lease you did not sign is not legal however you would have to be able to prove the signature he has is fraud. 

No, you don't need to spend any of your own money for this unless you choose to. You definitely won't have to take him to court.

Look up the Warranty of Habitiility law for your area. That's the info you need. If your area is one of the many areas that have such a law follow the instructions. If the landlord refuses or doesn't repair the heating system and the window contact your local code officer and ask them to inspect the place. They will handle it from there.

If the landlord offers to fix the issues give them time to do it. If it gets to the mess of getting your code officer involved be prepared. The code officer may not allow you to live there until the property is up to code and safe to live in.

Did you request repairs?

Why would he give you the old one to sign?  He gave you the new one - obviously.  So, those problems have been fixed, right?  Why are you still whining about it?

Work on your grammar and writing skills. That will allow you a better paying job so you don't have to end up at places like that.

You moved in without inspecting. Repairs have been done. What exactly are you wanting to sue for?

Are they fixed now?

you can try doing that