The vegetation now covered by water will start to rot and release lots of methane and other goodies. Unless it is cleared away first. This is only practical with trees though.
It is due to the decomposing vegetation under the water. However, it depends on what is under the water. Some hydro reservoirs actually are carbon sinks while others are worse than coal plants. You also have to take time of operation into account. Hydro becomes cleaner as time passes. A 50 year old hydro plant will have had a lot of the vegetation decomposed already vs a 5 year old one.
Not really. It's from rotting trees, and when they decompose in an anaerobic environment they take 3-5 times long to decompose. Most trees will take well over a hundred years to fully decompose.