Thanks, ZooK! My understanding is that jelqing can damage tissues.
Yes, although jelqing is a time-honored PE technique, because it is difficult for newcomers to understand how gently or how hard to do it, and because it is difficult to keep the pressure consistent, it can lead to injury. Beginners to PE nowadays are gradually being moved to safer techniques.
No scientific evidence for pumping (and yes, there are studies. Wiki is your friend).
There have been studies sponsored by the pump manufacturers and there's quite a bit of anecdotal evidence that pumping works, but pumping is mainly a girth-enhancing technique not a length-enhancing one. Some men find that their girth work helps build length too but the consensus is moving towards getting the length you want before tackling girth.
"Traction" seems to have some effect, but God knows what that involves in the way of equipment.
Extenders are some of the better-studied PE equipment.
What are the manual exercises you mention?
There's quite a few.
While the old-school PE forums like LPSG.org and Thunder's Place have their place, they're being supplanted by subreddits like r/AJelqForYou, and they have some pretty comprehensive FAQs and tutorials on the more-modern methods of PE.