It needs to be a closed mitre hip as suggested or an inverted hip. With the inverted you would have the left side acting like a valley and the right side hanging over like it is just now.
The lead also need to be a good bit wider than it currently is.
Just so you know that's not a valley they have put in. It's a bonding gutter, the fact they can't tell the difference tells you all you need to know.
https://hambleside-danelaw.co.uk/products/dry-fix-bonding-gutter-high-profile/
If the roof is off it comes off no problem. If you just want to patch it to hold it up you can use wood to hold it up, just cut it and secure it in between the trusses.
Not necessarily, depends on experience with that one. An older lead worker is more likely to boss it instead of pulling all his gear up for a small job. I'm aware due to being a leadworker.
My city and guilds training course was a 5 day one and we certainly didn't use code 4 for a hopper.
11 is maybe too low for slates unfortunately, you can use this https://www.permavent.co.uk/products/easy-slate/ which can go to 12 or 10 with cement fibre slates