If a child is saying "mine", I let them know that it is actually a daycare toy and it is "5LM's toy" and I want all my friends to share it or it will have to go away. Now the kids tell each other that it's a dc toy or 5LM's toy and I very rarely hear "mine" anymore!

Pushing, biting and hitting are all things that would result in a time out here. I have had one child who time out didn't work for so I would took away something she loved. In her case, it was the pink chair. I have two green and two pink and if she wasn't behaving nicely she didn't get to sit in the pink chair. It worked MUCH better than time outs were working.

I don't make the kids apologize. I encourage it and teach them when it's appropriate to be said but I don't force it. A forced apology means nothing in my eyes. I will say something like "xxx that is not nice behaviour. It would be nice if you apologized to xxx for doing yyyy" and than leave it as is. If they apologize, great! If not, it will come in time!