is a contract signed but with a pen written amendment on it legal?

When you changed the contract before signing, and sent it to your prospective landlord, you made a counteroffer (the initial contract proposal was an offer.)  The question is whether the landlord accepted your counteroffer, which he/she/it could have done by signing the amended contract.  Even if the landlord did not countersign, if the parties continued to act as if they had a contract (e.g. you continued to pay rent, the landlord continued to allow you to occupy the space and kept supplying heat, etc.), there is a good chance that a Court will find that a contract was formed.