The following is assuming your specialty uses ERAS (which most do):
most programs that I've seen do not specify the number of letters you can submit; that said however, I wouldn't send more than 3-4 unless they REALLY add something to your application
the process is that you have letters sent to your Dean's office and they upload them to the ERAS server. When it comes time to apply to residency programs you pick and choose which letters go where (ie, if you are applying to multiple specialties, you might have letter from Dr. X go to Ortho program Y, and letter from Doctor Z go to General Surgery Program Z). Obviously you don't see copies of the letter in most cases and most students, applying to only 1 specialty, submit all letters to every program to which they apply.
Therefore, given that the letters are submitted to ERAS and NOT individual programs (programs will actually say they don't accept documents outside of computerized ERAS applications) they should be addressed generically (ie, Dear program director).
if you have a special connection with a certain program (ie, your father is an alumni), it is obviously ok to have that letter addressed personally and submitted through ERAS. In such a situation THAT letter would only go to that program (and none of the others).
Do not ask your writers to send multiple personalized letters unless you are only applying to very few programs or they offer to do so.
Your Dean's letter is not released until November 1 (usually) and as such, is not usually available before then either. Therefore, I imagine it would be available too late to be of benefit to your letter writers. Presumably your letter writers know you well enough and when armed with your CV and personal statement should not need additional information. Ask they if they would like such but I imagine they will say no.
In short, you do not need to provide more than 1 envelope for your letter writers to send the letters back to your Dean's office (check with your Dean's office as to the appropriate place for the letters to be sent). You don't say what stage you are at - don't get letters too far ahead (ie more than 1 year); they will need to be updated. You can ask letter writers to write something now while you are fresh in their minds but tell they you will be asking for an updated letter when it comes time to apply. If you are a first or second year student, remember that clinical letters will be given more weight than those from basic science faculty.
Hope this helps.
PS. I would NOT ask for copies of the letters although some writers may offer them to you. It is expected that they are confidential. However, it should be the duty of your Dean's Office to read these and inform you that one (or more) of your letters does not strongly support your candidacy should that be the case. Letters in which you are aware of the contents are seen as less truthful and more suspect than those kept confidential. Ask your Dean's office to let you know if any of them are less than flattering.