I have never ASM'ed, so I cannot give you "ASM'ing from an ASM's point of view" - however I can give you "What I expect from my ASM's from a SM's point of view" - and I have experiance with lots of shows with little to no rehearsal (or planning) time.
What is expected of an ASM depends a lot on the structure of the cast and the SM. Basically, the ASM does the jobs that the SM either cannot, due to logistics, do, or tasks which the SM wishes to delegate. For example, one prime duty for ASM's is props. More often than not, the ASM will be responsible for presetting the props on stage, ensuring the props are all on the props table when not in use and basically that everything is in order.
When thinking of the stage manager, I find it best to look at them as the center of communications. During rehearsals, they keep notes on blocking, script changes, incorrectly spoken lines, directors notes yadda yadda yadda. Then they distribute them as required. They also provide a center-point for the production team. They are also responsible for a lot of the 'grunt' work. They make sure the actors are happy, the directors are happy, the designers and crew are happy. They make sure things run to time, from the overall production schedule to the timing during a show.
It is a rather involved job, and the role changes from company to company, cast to cast, show to show.
From my reading of the excerpts, you will basically be 'cheif deckhand and props master', however the SM really has not defined the duties - ie do you have to create the deck sheets and prop sheets, or will they be provided?
It sounds like a good type of 'thrown into the deep end' type show, if you pick things up quickly, then it is a great show for you. However if you are worried, I would suggest working on a show with a decent rehearsal period so that you can learn where you fit in.
Shows with little to no rehearsals are really fun if you enjoy presure, however you need to pay really close attention to how things run. Going for a drink or to the toilet during the rehearsal is definantly a no go, so make sure you have everything you could possibly use with you. Because there is no time to repeate things. Take concise notes, work out some form of short hand after you know what your job will entail if that will help. And if you don't get something, get clarrification, because the extra 2 minutes of clarfication may save 10 minutes of repeating the same sequence to get things down pat.