Q2 Visa to China with intent to apply for temporary residence permit. Will reside with Chinese wife

I am a US citizen in the US and am married to a Chinese National. My wife still resides in China. I am considering applying for a Q2 to visit my wife with the intention of applying for a Temporary Residence Permit after arrival in China.
My questions:
1. A Letter of Invitation from my wife is required to accompany the Q2 Application. The Invitation Letter must include entry and departure dates. I do not have flight reservations yet. Must the dates on the Letter of Invitation correspond exactly with my flight dates or can dates be listed as on/or about?
2. Will a 30 day Q2 be enough time to get the medical exam and apply for the Temporary Residence Permit? Is Q2 the best option in this instance.

Thank You-