Updated June 18 in response to Brenden's second answer on June 17:
First of all, thank you Emma and Brenden for trying to answer my questions! Both of you are right but here are the answers to all of my questions (feel free to correct me if I'm wrong):
[Q]: What about Searching? The query parameters are stored in the URL. Should I disable view state in this case?
[A]: After doing some trial and error with the "Smart search dialog with results" web part, I've concluded that you should not disable the view state. The reason being that the "search mode" filter quits working. However, searching and paging still work.
[Q]: Are BizForms/Web Forms the only web parts which require an enabled view state?
[A]: After doing some testing, it doesn't appear that these web parts need view state enabled. However, they were very simple web forms. Refer to Brenden's second answer below for cases where a form would need its view state enabled to work properly.
[Q]: What happens to the web parts within a web part zone if I disable the view state of a web part zone?
[A]: All web parts within that zone disable their view state, as well.
[Q]: What happens to the widgets within an Editable Text web part of which I have its view state disabled?
[A]: I haven't tested it but I'm pretty sure their view states get disabled, as well.
[Q]: Generally, should more web parts have their view states disabled rather than enabled?
[A]: This is something that you'll discover on your own as you pour through your site checking if every web part requires view state to be enabled.
[Q]: Why can't I find this information anywhere?
[A]: I'm not sure exactly why there is no documentation on view states relating specific to Kentico. I had to investigate this stuff on my own through trial and error to learn it. The best general resource that anyone has been able to provide me is this documentation which is what I have linked in my original question. For example, where would I have learned that web parts with their Visible property set to false affect the page's view state size? Furthermore, if a web part uses a visibility macro then that affects the view state size, as well.