First things first - I’m not a doctor, so take everything with a grain of salt, but I’ve got some experience with needles, scalpels and other funny stuff.
This depends A LOT on who is doing the install… 
The risks you mention can be mitigated by letting someone do it who is experienced and routined in the field of surgery or bodymod - a self install is definitely not a good idea when a scalpel is involved (in general).
It would be pretty bad if they were severed, but that’s something that would be extremely unlikely if the installer knows what they’re doing. What happens is that some of the little veins get poked, that’s why it bleeds, but that’s something your body can usually handle on its own - though you shouldn’t take things like blood thinners before, obviously. And some of the little nerves might get hurt or irritated as well, and they might need some time to heal, but they do. I was one of the persons who had a numb spot above the flexNExT, and one of my actually pretty standard p0-glassies had a tingling sensation for a while. Both of that went away after some time, though to be honest, nerve damage requires patience.
Both (good) surgeons and (good) bodmod artists know how to avoid that. I have a subdermal implant on my wrist, sitting directly above the tendons, as well as a scarification that has one of its main lines running directly along the big, blue vein you can see on your forearm - no problems with any of that. It was a strange feeling to have someone poke around in my wrist, and I was a bit nervous about my tendons as well (was my first implant after all), but those people know what they’re doing. Go to a pro, and you’re most likely safe
Infections can always happen, as you wrote yourself, as well as rejection - take good care of yourself, go to the doc / bodymodder if somethings looks or feels really odd, and you can reduce the risks a lot.