implantation questions.

When do you get implantation bleeding? When's the latest? Would you test positive for pregnancy before the egg implants or after it does? If sperm can live for 7 days in the vagina could it be possible for it to get to the egg on the 7th day and then 6-12days after the last day can you get implantation bleeding. My period is about 7-8 days late and I got negative tests but I just went to the bathroom and I had some brownish discharge like my period was starting. Not sure if it is or if it is implantation. Thanks!