Sounds like all of that needs to be fixed. Missing bolts would result in an out of balance condition and cause vibration.
Missing clips on the u-joints could cause early failure of the u-joints.
Loose u-joints often make noise, and should be replaced as soon as possible.
Regarding the squirrely feeling, driving in front wheel drive should not have a significant impact on handling, though it may be easier to break a wheel free. You may want to check out all the front steering, trackbar, and control arm joints and linkages for play or looseness, and also do an alignment if necessary.
You can do the u-joints at home with a large socket set and a good hammer, or with a ball joint press. Plenty of videos on YouTube showing how to do it.
This forum generally recommends the Spicer Life series sealed joints.
Post some pictures if you canIt has some kind of adapter at the end which makes it really hard to hammer out, at least I think.
There are multiple videos on replacing u-joints with just a hammer or a vice (if you have one). Here's one and another and another.
As for the tendency to run awry when you hit a bump while running "front wheel drive", you may be suffering from classic bump steer which is caused by improper steering component alignment. Do you happen to have a drop pitman arm? Search for "bump steer" for more info.
I had a very similar issue, It ended up being the front bearing retainer was broke in half. The front part where the throw out bearing ride on, was spinning with the input shaft, I thought the front bearing was bad. but it wasn't.
Yes. You could have damaged bearing, gears, or both.I was driving the other day and I noticed a grinding with some struggle to accelerate. I drove a short distance to a parking lot, and during the time the grinding feeling got worse. I checked the rear diff fluid and it was down a full quart even though I had filled it up less than a week prior. I'm not sure if something happened there.
Could the baseball card in the spokes sound been related to the rear diff?