Unfortunately, if the five adventure dives are done with one shop and instructor and then the specialty is done later with a different shop and/or instructor, the adventure dive (even if in the logbook) may not be counted. The PADI standard says the dive "may" be counted, not "must" or "shall." So it is worth checking with the new instructor before making the assumption the dive will be counted as one of the 3 (for Navigation) or 4 (for Deep) for the specialty. On the other hand, the price for the specialty might not change whether the adventure dive is counted or not, so you may as well just do the dive over; you will most likely learn something from it.What's "recommended" varies based on who you ask.. lol.
No dive from your AOW (or adventure dives) is "wasted". They are logged in your dive log and count as one of the required dives if you do that specialty later (so the deep dive from AOW is one less dive you're required to do as part of your deep diver specialty course for instance).
Yes, you are exactly right. I was wrong in what I said earlier. In fact, the new manual is mandatory, because there is now a section in it called "Thinking Like a Diver" that needs to be covered as part of the class.There is an AOW manual now. I used it for my AOW course earlier this year, and you can buy it here among other places (I got mine from the dive shop I did my AOW course through).