I'm not sure exactly what date in May the application opens, so it might open before you leave, or it may be a few days later. (The AMCAS website might have this date up, so I'd check there)
If you pre-write everything now, it will only take a couple hours to complete (I would type everything into the application, not copy and paste bc there could be formatting issues. If you do decide to copy and paste, do it in a program like TextEdit that doesn't have formatting). Make sure you also have an official copy of your transcripts printed out, so you can input all of your classes using the same course names, #s, etc as those that appear on your transcript.
Once you start filling out the application in May, you will need to request transcripts and LORs sent to AMCAS. You also need the AMCAS "cover sheets" for these, so you can't request them before you start filling out the application (they will have your AMCAS ID, etc on them), but this can be done as soon as you start filling out the app. This part of the application may be harder to do while you're abroad, since it has to be done through the mail. If you have someone in the US that could do this for you, then being abroad shouldn't be a problem.
In regards to secondaries, you only need to include one school when getting the primary verfied. If you just include one school, then you can add the rest of the schools when you get back. This way you'll only get one secondary at the end of June/beginning of July. Once your primary is verified, if you add schools, they will get your primary that day/the following day, so there won't be any delay in them receiving your primary.
For secondaries, I would try to complete them within a couple of weeks, but it's better to send an edited essay "late" than sending an unedited essay early. I think it also depends on how long the secondary is. For short secondaries, I sent them in within a week or two, but I sent my Vanderbilt secondary after 4-6 weeks because it was longer/more involved and I had secondary burnout (and I still got an interview there). I would try to complete most secondaries by the beginning/mid august. Also, check out school specific threads to determine which schools start sending out interview invites early, and complete those secondaries first. I know Michigan and Pitt, in particular, start sending invites pretty early.
I hope this helps! Let me know if you want further clarification, or if something I wrote is confusing.
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