Short answers to your questions as follows:
 
1.NO
2.It totally depends. 95% chance is that, it's not required since BC criterial already met
3.Standard documents such as new agreement, insurance etc. Local Foreign office can give you detailed list
 
Once you get the new contract, get the legal work done and then resign. There is a possibility to have 2 zusatzblatts until Sep 1 if they are OK with your employment status.
 
Having said all these, the ultimate authority would be your Foreign office case officer. So better, be in touch with him/her upfront.