Rip the lot out and start again...your plumber is a cowboy.
Probably had a heart attack from the stress of his previous customers complaints.
Chuck out the bodged pushfit and compression fittings and use solvent weld waste fittings (and prepare them properly with the cleaning fluid).
Re-do the copper pipework so that it's suitably supported and insulated as necessary ie so thay don't bang/resonate with the water flow and the cold potable water isn't heated by the hot pipework.
The aluminium safety tag must not contact the copper pipe.
Chuck out the flexible pan connector...it's a sure sign of p**s poor planning. Use proper purpose designed fittings not a diy effort.
As for fitting the waste pipe through the center of the joists will the gradient be correct? Will there be sufficient room for thermal expansion etc.