If I'm reading the question correctly, you're asking if you need to reuse the biggest stock spring? If so, yes you will with the 3k and 4k kits that I've seen. That is also known as the idle spring. I have no experience with the 5k ones but it sounds like they come with a new idle spring.
As for shims, I have always removed all of them and have had no issues doing so. I have never checked it, but I'm guessing that there is not enough change caused by the shims to make it worth retaining them.
After dealing with several different pumps, I've found that different ones also like differing amounts of preload on the springs too. I always keep the preload even on each side, but how much will vary. Usually I end up leaving them set somewhere between 3 and 5 clicks after the initial one.
The only way to find out what your pump likes is by playing around with it. Try some different stuff, you won't hurt anything.
I too prefer going in from the side of the pump to do governor springs. I've never figured out why people think it is easier to reach down from the top, but to each their own. I think going in from the top would promote dropping something. Then you get to go fishing.