tourist visa extension for German citizen

Hi I'm on a tourist visa which will expire on 9th Sep (Saturday). I want to stay as long as possible in China, so is it still ok if I apply on 7th Sep (Friday) for a 1-month singe entry extension or is it too late? If I apply on 7th Sep, will my new visa be valid until 7th October or possibly longer/shorter...? I need to book my flight back to Germany soon and it would be very unlucky to have my flight booked for 7th Oct when my visa could expire on 5th Oct or sth...

Further I entered China in June from Guangzhou and have and will keep on staying at a friends place in Guangzhou. End of August however I will go to Beijing. So, if I stay in an accredited hostel a couple of days before my application in Beijing to get the temporary residence permit, will the PSB not ask me where I have been all the time before and ask for a temp residence permit from my time in GZ?

Thanks alot for your help, very much appreciated!