Your membrane will not self seal around the nails.
Ideally you should fix counter batten on the ply then membrane and slating batten.
The facia should have a vent on the top and you should fit an abutment vent at the top of the slope with a lead flashing over it.
Screwing the ridge tiles directly into the ridge tree is fine.
It is quite likely that they could not fix an extra timber under the ridges because it would have made the ridge line too high and cause the ridges not to sit properly .
As said by Mackie the problem is almost certainly being made by the wind at eave level.
If the underlay is going past the bottom course into the gutter then try cutting it back with a sharp knife.
If this stops the noise then you need to look at having underlay support trays fitted.
Your first cut is cocking up because your lead saddle is over the adjacent tile that the cut should be interlocked with.
Also your saddle is not dressed sufficiently.
It sounds quite reasonable.
They will need to buy a 6m roll of 600mm code 5 lead,
Bidding felt, gas and oxygen,
Copper nails.
Maybe copper clip and also patination oil.
Buy a decent tile scribe, like you would use on ceramic tiles.
Scribe the slates 2 or 3 times and snap them on the edge of another slate.
One scriber should easily do you.
The grp does need to be taken up an upstand higher than the ridge tree.
A dry ridge system could be used as long as the grp is sorted out.
It does really want an experienced roofer.
The ridge needs to come off first. When the ridge is off you will probably need lead saddles formed between the flat roof and the tilling at the corners, the fat roof will probably need extra fibreglass over the lead saddle and ensure that the grp goes up an upstand under the ridge tiles before...