Sounds like the police approach is a bit rough around the edges Colleen?!
As far as talking goes, I think its fine in your own dojo if it is aikido related and if they are questions. Problem with my dojo at the moment is that there are no high grades. Therefore it is very serious work trying to instruct because sometimes it is the first time EVERYONE has ever done a particular technique and therefore a bit of discussion between them saves me going around everyone individually to sort things out.
Unfortunately, everyone at the start develops bad habits, but this is what aikdio training is about isn't it; getting rid of your bad habits?
Also, I find talking provides a more relaxed atmosphere esp. if it is mildly humerous.
Its probably up to the sensei what he thinks works best with the group. If people are just chatting about the weather they are either bored, not focusing on what they are doing or not interested in aikido - either way the sensei can do things to prevent this situation.
As far as students giving instruction when you're not training with your regular sensei goes - pretty much out of the question (unless they are absolute beginners who are being shown, and they can't do anything). Basically if you're there training you're there to learn how someone else does it; I've seen people train for a solid week and not learn a thing because they are still trying to do what their previous sensei told them.