That is poor.
Hard to know what to advise here, if you rip it all out you are left with the straight chase gashed into the brick faces. That's gonna look awful pointed in.
Might just have to stick with the straight chase, but neater.
Best way to join is with a bonding gutter or lead as you said.
No, that roof will be perfectly water tight, just looks a little poor.
A few little things let it down.
Looking at the rest of it now on those pictures it doesn't actually look too bad.
Just a couple of minor aesthetic issues as you said (slightly messy pointing etc)
The tiles are straight, it's next doors that's a bit pi*sed up, they could have straightened the rosemary's up a bit.
Don't let them anywhere near your roof...
Everything looks twisted, they havnt even bothered to put next doors cut tiles back properly.
Pointing, disgusting.
Leadwork, ok.
And that's in one little picture, would love to see the rest of it.