Yes, you can include your lease on your Chapter 7 bankruptcy. You will be required to accept or reject any outstanding lease at the time you file. You can choose to reject your residential lease at the time of filing. Any past due arrearage will be treated as an unsecured non-priority claim and will be discharged with your bankruptcy.
If you stop paying your lease before you file, you are open to collection calls, lawsuits, and possible garnishments. You will only receive protection once you file your case.
Yes, you are required to list all creditors and the landlord would be a creditor, even if you are not behind in payments. You should list the contract on Schedule G - executory contracts and unexpired leases. The Chapter 7 trustee will take over your position with the landlord after you file. The trustee will determine if they want to assume the lease - in this case most likely not.
If the trustee does nothing, the lease is automatically rejected and the landlord has a general unsecured claim for whatever damages exist at the time of filing. Since the landlord's claim is an unsecured claim, your liability will be discharged when you receive your discharge.
Not only can you break the lease, but all debt from the lease would be discharged. You must list the landlord on your petition. Also, if you stay beyond the date of filing, you may be responsible for the rent post-filing until you leave (or are evicted).