I wouldn't be too hasty to get rid of anyone just yet, though it's entirely your decision to do so. Obviously the later round picks might be of no interest to you at all so swapping them out isn't a big deal.
In the case of waivers, right now it applies to all players in our league and all teams. After the 28th, all those players on the free agents players list will clear waivers and be free agents meaning there won't be any wait time to pick them up.
Using your example, if we all want Battier, we can all put in a request and the person with the highest waiver wire ranking (lowest number) would get him. The waiver wire order is set in reverse order to the draft order, so Rob has #1 and John has #8. Once you use up a waiver wire request, you drop to the bottom of the list (#8) until other people use their waiver wire priority up.
If you drop a player he will go to waivers for a couple of days before anyone can pick him up. If it's a desirable player and multiple people try to get him, the player will go to the player with the highest waiver wire priority (again, lowest number). If no one wants him and he clears waivers, he enters the free agent list. Free agents can be added by anyone at anytime and there is no waiting period, you get that player right away (though they won't show on your roster as eligible to play until the next day).
Clear as mud?
Oh, and my team is too big. 
Actually Brent, that made a lot of sense. I just don't get some of the details when reading Yahoo's Fantasy rules and help area for Rotisserie. I think I'll start picking up the game, strategies, and nuances of play here when the season starts. I appreciate your comments.
I noticed that Shane was picked up by Rob, so that must have meant Rob also wanted Shane and Rob had a higher waiver priority. Is my starting 5 the top 5 positions on my team list? So my "PG", "SG", "SF", "PF", and "C" are the only players who will accumulate points based on their performance, and all my "Util" and "BN" are not in effect?
Gasol is on my team, and this was on the Fantasy News and Notes area:
Oct 27 According to the Memphis Commercial Appeal, Gasol still hasn't been cleared to participate in full-contact practices because of a sprained ankle.
Advice: Gasol told the newspaper "it was no mild sprain," but remains hopeful that he'll be ready for the season opener Oct. 31 against San Antonio. When healthy, Gasol is a top fantasy option. He averaged 20.8 points, 9.8 rebounds, 3.4 assists and 2.1 blocked shots in 59 games last season. So if Gasol doesn't play in any of the games I have him in the starting 5, that means I won't accumulate points for that position, right? If that's the case, is the strategy to put someone in place of Gasol to get for sure points?
Sorry about these basic questions, but I had to ask. Thanks, King