It takes 6 weeks after taking the exam for your scores to arrive at the school. Most programs will not care about your GRE scores being late (double check the website of the programs you are looking at). Basically anything that YOU are responsible for showing up needs to be on time or close to on time.
In terms of taking it 3 times: it's only worth it if your score is going to go up each time. However if you're talking about taking the October and November tests, then you can take it 3 times and not worry about reporting all 3 scores. Basically it works like this: the ETS reports ALL scores for a particular test (e.g. reg GRE or PGRE)* when you submit the request. However, they ONLY submit scores that are already graded at the time of score submission request**. So if you take the October exam, you can report your 2 sets of PGREs to schools right when you get the October results back. Then if you get the results back from the November PGRE and find out it was better than your previous scores, you can submit it at that point. Unfortunately, this scheme will cost you more money, but it is a nice safety mechanism.
Schools will not need to know you took it 3 times unless you decide to tell them you took it 3 times.
*What I'm saying is, if you request your PGREs to be sent, they will send JUST your PGREs, but they will send ALL your PGREs. You can however submit requests for PGRE and GRE to be sent together (which is a cheaper way to do it).
**You can request unsent test scores to be graded, but they will not be sent until after it is graded. To do an immediate submission, they will not include any future tests automatically.