1. The water parks are never crowded like the theme parks, so you'll be fine. The first 60 minutes BB is open you can do pretty much anything you want with no wait at all. Since it won't be summer, you will find it even less crowded.
2. No. Even in the peak of summer, there is more than adequate seating. There is no "best" area to get a seat, it all depends on where you want to be. Ski Patrol and Tykes Peak aren't as busy as you may think. If you're there at 10am you'll have no trouble getting a spot anywhere.
3. Personal prefence. I absolutely despise pool shoes, they are n-a-s-t-y in my opinion. But that's just my opinion. In the heat of summer, the pavement can get hot in spots...though much of it is actually continually sprayed down to keep it cool. However, in October it may not be as big of an issue. If you wear them, you have to take them off on body/tube slides and hold them in your hands.
4. No, absolutely waste of money in my opinion. Again, just my opinion. See my answer to number 2 above for the reason. Paying a ton of money for a chair when there are endless free ones makes no sense...but I'm admittedly a cheap skate.
Other things to add... The water parks are a ton of fun. Like I said, the first hour has the shortest lines. Summit Plummet, Slush Gusher and Downhill Double Dipper (DDD) lines build the fastest. Do those first. Summit and Slush are next to each other, they literally share a walkway to the entrance. DDD is a bit away, but not too far. Teamboat Springs (family tube ride) is a blast. Lazy river is fun. Wave pool is OK, but nothing in comparison to Typhoon Lagoon. There are a lot of stairs...be prepared for lots of climbing. Don't waste time on the ski lift, maybe do it once for experience, but beyond that it's slower than walking and stops VERY often. Either rent a locker or don't bring valuables in. We've been to the 2 water parks a total of 50 times...at least...and never had anyone touch our stuff, but then again we only bring in old clothes, towels and some food. So if someone really wants to steal that stuff, have at it. Oh, and don't rule out Typhoon Lagoon instead of Blizzard Beach. Don't get me wrong, I love Blizzard Beach, but TL is just as awesome, if not more. Your kids, especially the 10 year old, are on the older side of Ski Patrol age group (meant for kids 3-10 or so). TL has a wave pool that's absolutely and completely amazing and worth the price of admission itself. It also has 2 family tube rides, where BB has one (though an awesome one) and Crush Gusher...which is sort of like a water park roller coaster.