Problem with the Omnitrix being alien tech, we literally don't know what material that is.
It's probably alien matter, considering it can go from metallic to symbiotic to elastic to whatever form the watch is under.
For the energy, according to the wiki: "The Omnitrix is powered by a special self-renewable power supply that will long outlive Ben." I think it means whatever energy source it is, it can never die out and will always renew itself to find energy to recharge the watch
Yeah, pretty much. His body still functioned even though he wasn't there anymore. It's like when Gwen separates from her body to go inside the watch, she isn't dead, but her body has no life in it anymore.