Hi!
Well, I'm by no means an expert, so take what I say with a grain of salt, but this is what I understand.
Some secondaries are already out, but really not very many. Also, because of how early in the process it still is, a lot of glitches seem to be happening (SLU and GW come to mind) so not everyone is receiving the applications and not all applications are working smoothly. I'm applying to 29 schools and only received 2 secondaries so far, and the notice from another school that they got my AMCAS and the secondary will be out in a month. So, don't stress! July is PLENTY early to be sending stuff out. In fact, I'm pretty sure a lot of universities are still working on their waitlists and such and aren't really in new-class mode, so they won't even be looking at the secondaries for a while.
As for AMCAS verification, it has nothing to do with LOR's, so don't worry about it. You'll be verified without them (but you do need the transcripts to be in). I believe right now it's taking ~7-10 days for verification to occur once transcripts are in, but it seems to be a bit of a random process (i.e. not a straight-up first come, first serve).
Now, for exceptions. Some schools send you information (which may include the actual secondary) before your AMCAS is verified. My understanding is that AMCAS sends some basic bio information about applicants to their chosen schools even before verification, and a couple of schools respond to that right away and send a secondary (GW did that I think). This is definitely the exception, though, and most schools don't do anything until you've been verified (and until their secondary is ready, of course).
Also, remember that some med schools screen primaries. Usually, that means that they send secondaries to pre-screened applicants and then once they get secondaries (and LOR's) they choose those to interview. A couple of schools (Vanderbilt comes to mind) goes one step further and does a huge pre-screening of primaries and offers interviews to all students who get secondaries. Again, this is rare.
Ok, I believe that's all. Good luck!