1. Yes, thread it on by hand, riding it will tighten it as much as it needs to
2. flat side against the hub. there is a tool to remove it and it has four prongs, so the side the tool will fit into has to face outward.
3. if it fits either 1/8 or 3/32 then technically it is a 3/32 free wheel. Some chains have their size stamped onto some of the links otherwise, it is kind of hard to tell with an untrained eye.
4. the green stuff would be appropriate, but I put on and took off plenty freewheels on my BMX bikes for years with just a little WD40 (not advocating it, but it is possible if you are in a pinch)