1. Correct!
2. I'm not sure if I understand this scenario. If this is in reference to something like filling up a glass of water to the brim and then putting in an ice cube (or more water), then yes, the water level rises.
An example I like to use to remember this is the melting ice caps!! Hey, what fun!
If you thought of a glacier positioned on top of some land and some piece of it broke off into the ocean, the level of the ocean would simultaneously rise as a result. It matters not if that hunk of floating ice melts or stays an iceberg, the rise in the ocean level has already occurred and will not change unless you are able to take out that oceanic ice cube. (Example excludes some factors, including any effects due to the ocean's salinity)
