Below is my understanding of NJ tenant law and what I would do if I were in your shoes
@Sandy S.
According to NJ law:
1) Does a tenant's non-signing of the lease automatically turn into a month-to-month lease?
If the landlord doesn't offer to renew the yearly lease, then the lease will automatically turn into a month to month lease. However, in your situation, it is a disagreement on the leasing price, I would think in this situation, your tenant should vacant the property by the date the lease is over.
2) Do I have the right to not renew the lease, given that I do not agree to their counterproposal?
Yes, you do. Generally, for yearly lease, you need to provide them 3 month notice of new lease term or termination of the lease. For month to month, you only need to provide 30 day notice to terminate the lease.
3) What time frame do I have to give them to vacate the premises?
In this situation, I would categorize your tenant is on a month to month lease and i would give them a 30 day notice to terminate the lease and move on if that is what you want to do.
Hope that helps. Good luck!