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1. Is a month's notice not enough to move out. He says I am bound by law to pay till the lease expires or he finds somebody else. Am I legally bound to continue paying even if I don't live there?
Your landlord is quite correct. You signed the lease and are bound by it.
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2. Provided that I leave on time next month, do I need to pay next months rent now, though he has my security?
If he hasn't waived payment, you must pay as required by the lease.
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3. Does my right on full/part of security change whether he finds someone or not?
When he finds someone else to rent the premises, your obligation may be reduced. If so, it is possible that you may get part of your security back, but not likely. Your questions suggest that you are mainly concerned with your security deposit; but please understand: you are responsible for rental payments through January (assuming the landlord fails to find another tenant), not just the deposit.
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4. Can he sue me if I leave and he has the rent for the duration I stayed + security?
Certainly. You owe him for all lease payments through the ending date of the lease, unless he can find another tenant. And of course he can sue you for this.