Actually a tilemap layer can be smaller or bigger than the canvas (in Auto mode tiles will be created/the tilemap will be increase its size when it’s required (in manual mode the tilemap size keeps it size/doesn’t grow automatically).
Yes, I think the only way to fix this in using rgb mode or indexed mode but adding a new color and setting that color as the transparent index from Sprite > Properties
At the moment it’s not easy, one possibility is to convert the tilemap to a regular layer again (Layer > Convert To > Layer), then change the grid size (View > Grid > Grid Settings) and finally convert the layer back to tilemap (Layer > Convert To > Tilemap).
Yes, but there are some features missing to handle tilesets easily. At the moment the only way to share the same tileset between two tilemaps is duplicating a tilemap (Layer > Duplicate menu).