I'm relatively new to cycling, so haven't had a lot of experience on different bikes. Given that my interest is primarily in vintage, I figured this would be an appropriate place to ask (plus everyone here is great)

I've heard my UO-8 has 'relaxed' geometry. What exactly is this referring to, and how does it affect my ride? I've also heard such and such 'with that fork rake' - what does this mean?

Does lugged vs. welded steel affect ride/handling? I think mine is considered 'gas-pipe', is steel really that much more bump absorbent than aluminum/Ti/CF (maybe this shouldn't be in the vintage area )

Very strongly. The frame and fork contribute to how the bike feels when you ride it, especially when you hit bumps or the parts come under stress. The materials also have much to do with how it handles, remember. The geometry of the frame is how big the angel in the frame is. Take a look at a racing bike and compare it to a Raleigh DL1, for example. The Raleigh's angles in the frame aren't as sharp and hence are termed "slack". Frame angles usually help to dictate the distance between the wheels. The closer together the wheels the more responsive the bike is and the tighter it can corner, I have found. The cost of this is some stability. A DL1, which has very slack angles, is very stable but doesn't coerner horribly well. A racing bike will be less stable in terms of hitting bumps and rocks but can corner faster and is more responsive.

In your case you have a UO-8 with relaxed geometry. This means that, relatively speaking compared to bikes of a similar type, your frame angles aren't as strong. This sacrifices a little performance for comfort and stability. A good road bike, for example, has a little slack in its angles to help the rider stay comfortable and to cope with rocks and bumps. A utility bike used for commuting in rough conditions will have very slack angles to cope with poor roads and help the rider stay up.

Steel welded vs lugged: Yes this affects the ride but not nearly as much as your frame type and material and wheel width and size. Welded generally has less give to it than brazed because the brazing material is usually softer than the steel bars. In the old days, cruisers were welded and the frames built like tanks. 60 plus years later they're still around because no weight was spared making them welded and built to last. I generally prefer Brazed and Lugged though, like an old Raleigh. It's strong but not so heavy and looks great.