Good questions.
3 weeks out, if you are still trying to lift your score, then you do want to tackle whatever you think your weaknesses are. Note something else: one key area of weakness is careless mistakes. Everyone should expect to have 1-3 in each section, but if you're making more careless mistakes than that, then that's the place to start. You already know how to do these, so fix whatever issues are causing the careless mistakes and you will start to get these right!
Here's how:
http://www.manhattangmat.com/blog/index ... -the-gmat/Starting about 10 to 14 days out, your score should be where you want it to be (you can confirm this by taking a practice test under 100% official conditions, including essay and IR). At this stage you'll move to a comprehensive review. That is, you're no longer trying to improve weaknesses; instead, you're doing a final review and getting ready for test day.
Here's how to do that (two articles):
http://www.manhattangmat.com/blog/index ... an-part-1/http://www.manhattangmat.com/blog/index ... ew-part-2/The articles above address your question about when to take the last practice test, but I'll also answer here. My recommendation is to take the last test 5 to 7 days out. Others are a bit more relaxed and will say 3 or more days out - but I think that's too close. You don't have any real time to work on anything and you risk tiring yourself out close to the test.
Good luck - let me know how it goes!