On a hard floor yes but on carpet I would have reservations on it .It might crack.
Not recommended: it is too easily scratched. Better to sand the plywood smooth, stain it to taste, and finish it with a two-part epoxy.
Yes. However, the more common approach is to put 5/8" sheetrock on the bottom of the joists,and you can then blow in as much insulation as you want.
Probably. I would use plywood for this, at least 3/8" thick/
Yes -- but, unless the subfloor is really rough, you don't need to cover it. The foam padding which is used underneath laminate will deal nicely with minor roughness.
This should work. For this application, attach the panel to the wall with the rough side out so that the glue can grab on to it. However, this may not comply with fire code, which would call for 1/2" shetrock.
No. A twin bed frame should be made out of 1x6's, to which are attached (glued and screwed) 2x2's to support cross rails. Use 1x8's for anything larger. The cross rails should be 1x6's for a twin bed and 1x8's for larger, spaced no more than a foot apart. Either a mattress or mattress pad or platform can go on top of this. You can cover this assembly with hardboard, but I see little point in doing so.
Tempered hardboard is not the best choice for exposed surfaces. I suggest lauan plywood paneling, which comes in thin sheets, is not overly expensive, and has a nice wood surface which can be treated with stain or paint. It can be attached with small nails, but glue would be better.