1. When do I reapply? I am thinking to reapply by end of Jan is that ok (8 weeks)?
We know from experience that INZ take seriously applications with two to three months' GOOD evidence of living together.
2. When I reapply do I have to provide all the documents again?
Yes. The new application will almost certainly not be dealt with by the same CO, or even in the same office, as the previous one. In some cases, if evidence was retained, people have to send a copy and say, 'Original with my application to (whatever branch),' and give all the details, but it is much easier for the new CO to have the papers on his/her desk, and not have to go tracking back through the system.
It is good to remember that you are probably going to need the evidence of living together that you are about to send, over again, if/when you partner's visa is renewed so yours needs to be as well, or if your partner gets a work visa after the course is finished. So be careful to keep your evidence safe - send in certified copies and keep the originals, or vice versa. You will also need to keep collecting evidence as time passes. INZ routinely ask for more evidence just before issuing the visa (making sure that they aren't giving a visa to someone whose relationship has broken up in the meantime), then will need to see that you have continued to live together, ready for the next visa.
3. Also, where do I mention that I had applied before and got a visitor visa based on the partnership?
Write a covering letter.
4. What documents would be required so that I can have a strong point to prove we are living together?
See old threads for discussion and examples of partnership evidence.
https://www.google.co.uk/search?sour....0.lAngaoK--Rs