I once had an MOT fail for not having the inner arches welded to the outers - I'd had the outers replaced with repair panels, and they'd been done as a cosmetic job. I don't know how much difference it will make to structural strength and if they're covered in some way (mine just clearly stopped when you look up the arch) no-one might ever notice.
They should be welded along the lip of the arch, the bit that curls in after the double radius / mud trap part. I've seen various different ways of fixing the problem so that the rust doesn't come back, though I've taken the view that as I know the trap is there, it's something I need to keep on top of, rather than making it different in some way. As my arches are very poor, I've at least been in the position where I can put the repair sections on from the outside rather than welding 'up' into the wheelarch. I've been doing mine by test fitting the arch, making a 3-4" L-section, curving it, then tacking, then removing the arch and welding it properly.
The gutter section might not be quite so bad, because of where it is. If it was further up, it's also the only way that the roof is held on to the car along the sides, but because it's at the bottom of the pillar (that's the back in your photo, isn't it?) it just spot welds onto the bottom of the quarter panel edge. So you just need to strip the paint and drill out a few spotwelds allowing a bit of excess for the inevitable creepage of the hole, fix the panel, then weld the channel back on. Shout if you want a photo - I've done the same on the C pillar on the hatch, and although it's a different shape the principle is the same.