I've taken apart CPU heatsinks many times and I've tried beads vs. lines vs. spreading it out, after reading a lot of articles about it and seeing the results. Personally I prefer to spread it out on the CPU since I usually put a very thin layer which will just be enough to suffice without being excessive. I've opened my CPUs and GPUs after to confirm the spread and I'm just doing what I've personally figured out how to do it. Everyone has an opinion, go read some articles and form your own.
I think cleaning it is important, but it was very clean and shiny when I was done.
The GPU has bottoming out screws, you cannot put the cooler on as tight as you want. If you plan to squeeze the drop in the middle all the way to all the edges, you have to apply it liberally. I prefer to ensure it makes it everywhere and is sufficient. I have opened GPUs up after applying it to see what's happening, I suggest you do too when you are doing this for the first time(s).
When I put the GPU heatsink back on I line up the screw holes carefully and put it directly on. If you only use a grain of rice style you have to ensure it spreads (whether you twist it a little or try roll it etc.). Having opened up grain of rice type applications and seeing portions of the heatsink cover missing TIM has made me wary. To each their own.
Everyone has a point, and everyone has an opinion. It's best to try make the most informed decision possible since you can potentially wreck something. This was just one way to do it and a demonstration of how easy it can be.