Hi you will need sound proving installation underneath the floor boards expensive way but worth it or sound prove flooring underlay thicker you go would be more sound protection

I tried blowing the picture up and it looks like the frame of the door ( at the bottom ) does not meet the side strutt, therefore, the water goes around this and through the little gap. If this is the case and you'd need to take a close-up pic, then it's a design fault and i'd send the shower enclosure back to the manufacturer. There would be no way of closing the gap unless you made a piece of rubber of plastic fit the gap and glue it in place then mastik it.

Hi, Its hard to say without seeing it in the flesh or knowing the construction. One thing I would suggest is move the downpipe (first photo right hand side of window) and move it to the front elevation and add a spout so it feeds in to the gutter. At the moment it looks like it ejects on to your roof right by mortar bedded hip tiles which means the water is probably getting in under the hip (corner junction) and exacerbating the situation? Check the condition of the guttering on the main roof over the garage to make sure it isn't blocked or leaking at the joints too. Good luck!

A roofer will probably put flashing between the two extensions