As far as support is concerned, I have a carpentry book that shows joist and rafter spans for a given width; if you tell me how wide your room is, how wide your joists are (2x6, 2x8, etc.), and how many inches on center they are, I can tell you if you have more than enough support for extra weight. If you might need extra support, one thing you could do would be to glue and screw 2x4s flatly to the underside of your joists along their lengths to create inverted T beam-like joists. Your joist would work essentially as I beams, with the floor functioning as the top flange to resist compression, and the 2x4s functioning as the bottom flanges to resist tension and twisting.
If you're wanting to play fairly loudly, something should probably be done with the walls. The best idea is to start with the interior of the wall, and work your way out. Because you can always add greenglue after res channel, but not before, if I were you I'd cut out the wall as with the ceiling and use the channel you already have on the studs (if it's rc1). You can just do a single layer of drywall on the channel and add more later if necessary. Cost should be pretty low if doing it yourself, though time consuming.
The differential thickness I was talking about has an effect because of wall rigidity I believe. Thicker walls are more rigid, and as such, resonate slightly differently at various frequencies. As such, if a wall is built with varying thicknesses, it is more difficult for the wall leaves to resonate together. The info I have shows that this effect seems to be mostly noticeable in windows with their thin stiff glass panes, and less noticeable in walls and floors; so it may not make any difference in your scenario.
And finally, if there is no reinforced bed of cement for your tiles to lay in, that would suggest why the grout is cracking; to much movement between the tile and wood floor. You would need to remove the tile and either sand and finish your hard wood floor, or lay down some cement backer board and re-tile if that’s what you want. I have a background in construction, so I know at least a little about it. Also, if your joists and the spaces between them are made to support better, your grout will be less likely to crack as well.