Don't want to Renew can I month to month?

[BulliedinBrooklyn]

I live an building that is non-regulated. My one year lease expires September 1. On August 8, my landlord sent me a lease renewal with a 5% rent increase. Dealing with her has been a nightmare. I love the apartment but don't think it is worth the money in this economy. I don't want to renew but would like to stay (even if it has to be at the increased rent for those months) for 2 months while I look for another place. My questions are these:
1) did she have to give me at least 30 days notice before raising my rent?
2) do I have to give her 30 days notice before moving out?
3) I am entitled to say no to the lease renewal but stay on as a month to month tenant? Does it have to be at the increased rent?

Many thanks for any help. Also, if anyone knows of a great 1-bedroom in Brooklyn Heights or Park Slope pleae let me know!