I signed a month-to-month lease three years ago that has a stipulation in it saying I have to give 45 days written notice that has to end on the last day of the month.( at the time, I didn't realize that this is totally unreasonable)

Last year, the landlord raised my rent by 15% which is a huge increase. I never signed anything saying that I agreed to this but have been paying it. This landlord is negligent in upkeep and has been harassing me about stupid things on and off, ever since I have been here. 2 weeks ago, my indoor cat fell out of a window because the screen was so flimsy it fell off, and she is still missing. Last November my heater went out and I froze in here for 10 days because he was too cheap to buy a new heater, and he was waiting for some part from back east somewhere.

I gave written notice on Oct. 4th saying I was moving, and that I would like to be out by early November and I would give him a final date when I knew it. I stated that my last month rent that I already paid should cover October.

When I moved in, I gave first, last AND a $1500.00 deposit.

After the manager of the new place called my current landlord to check refs. I rec. a message from my landlord saying that if I planned on staying there would be a rent increase and I would get a notice shortly.

When he got my notice, he called and said that I owed him rent for the whole month of October, and that the last month rent I paid would be for November and that I am liable until Dec. 1st. To keep paying him rent. I said that was unreasonable, as then I would have to pay rent for 2 places and thought that it could be pro-rated from the date I left.
He then said that I should pay 1/2 the amount for October, and that I need to give an exact move-out date. He also said that he only has to give me notice to show the place, not get my permission.

What are my rights?

Sorry, no asking for a 45 day notice is not unreasonable at all, in fact many leases have 60 and even 90 day, although a lot of month to month are only 30 day.

But you are obligated to the 45 day notice that you signed and promised to pay.

So yes, when you give notice, you also have to give an exact date you move out, So if you have to end at the end of the month, you would owe for the entie month of Oct and the last month rent you paid would cover Nov rent that also has to be paid to cover the proper notice.

And of course he does not need your Permission to show his property. He only has to give you notice that he is showing it,

Also he merely has to give you a 30 day notice to raise rents on a month to month lease. So no your permission to raise rent is not needed either.

So you need to learn your obligations as a renter. The landlord is fully within their rights to everything they are asking