oh naysayers.....
i say do whatever the hell you want. if you already have a 105 group that you aren't using what's the harm in putting it on the bike? it's not like you can't move it to a different bike later if you choose to do so, just save whatever you take off the univega.
what's your reason for wanting to change the fork? you can't really do what you are saying anyway i'm just curious what's wrong with the original fork?
you have stem shifters. down tube shifters are, well, on the down tube
1_1/4" tires will fit with no problem
it's hard to spray paint a bike and have it turn out nice but it's doable with enough dedication, there are tons of instructables and diy sites online that will give you a pretty good overview of how to do it. unless the original paint is totally shot though you should probably stick with it. the odds of you getting a satisfactory finish on your own aren't great.
one last thing, it sounds like you might be best off taking the bike to a shop and having them install the 105 stuff for you, or if you are intent on doing it yourself you might check out sheldon brown, buy a good book (zinn is not bad and relatively cheap) and ask lots of questions in the mechanics forum.
good luck and enjoy the bike!