1. JPEG files are compressed files and worse than that, every time you compress (i.e., re-save as JPEG format) you lose a little information from it. Furthermore, JPEGs dont keep layer, mask, notating information in it, so, for the purpose of archiving your works, saving as JPEG is a no-no. It is ok to save as TIFF format, on the other hand, as TIFF files do support layers. BUT, make sure it's a lossless save. for me, i just save my post-processing works in PSD.
As for the question about 16-bit JPEG: it does not exist. Also, in digital imaging you should always remember GIGO - Garbage In, Garbage Out. Since your input is already a JPEG, you'll get nowhere even if you convert it to 16-bit. Think of it this way: i have a cup of beer. i pour in a cup of water hoping to have 2 cups of beer. well, i doo get 2 cups of beer, but the beer is now lighter and has an awful taste.
2. I'll leave this Qs for others to answer as ive never used Elements before
hope this helps