Almost every day there are 6-8 dead bees near the entrance--is this normal? I know that they will remove the dead ones from the hive, I guess I thought that they would take the bodies farther away? Is 6-8 dead bees a day anything to worry about?
A few dead bees is quite normal. A big pile of them might be of concern. I've watched my bees take out the dead (or not quite dead yet) bees and typically they drop right off the edge of the bottom board and that is where they stay.
Instead of an entrance reducer, I installed one of the metal mouse guards. We have LOTS of mice here, and it seems prudent to use one. The guard itself reduces the entrance some, but, seeing as many suggest that with a new installation an entrance reducer allows the new bees to defend a smaller space, I covered up about have the mouse guard with two pieces of electrical tape (one on each side stuck to each other so no exposed stickyness to trap bees....) and hope this will work. So my question is: any problem with doing this? How long should you use an entrance reducer?
You use a metal mouse guard because in the winter time the bees are clustered together higher up in the hive and they are not coming and going through the entrance on a regular basis. So the bees aren't defending the entrance. This time of year the temps are probably warm enough where the bees aren't in cluster anymore. They are coming and going and probably have guard bees at the entrance of the hive (assuming the temp doesn't drop way down again), so #1 I don't think a mouse would try and get in and #2 if they did the bees would probably kill the mouse. I think you would be fine just putting a regular entrance reducer on the small setting. Then again, I don't think you're hurting anything if you just leave the mouse guard on either.
I hadn't heard anything about screened bottom boards possible leading to absconding so I'll leave that for someone else!