1. It really depends on the situation. I am more likely to use "that" when it clarifies the meaning, or when writing very formal English. I also believe "that" should not be used with people (use "who" instead) despite its history. "that" makes people sound like inanimate objects to my ears.
2. If you eliminate "went", you would also have to eliminate "go". Both are useful words. In formal writing I may write "attended school" instead of "went to school".
3. Yes, "honestly" or "to be honest" imply that what you wrote before may not be honest. I would not use it in, say, a formal letter to an authority figure whose decisions hold sway over you (e.g. a letter to a potential employer or university admissions committee).
4., 5., 7., 11. I'd say avoid these in creative writing, but they're OK in expository writing.
6. "really" is unacceptable in formal writing, in my opinion. It goes along with "a lot", "boss", "kid", and other similar words that I believe should be avoided in formal writing.
8., 9. I find that the Chinese love to use "always" in their academic writing. I advise learners to avoid it (and "never") unless they're prepared to back up their statements with evidence.
10. Just know how "literally" is supposed to be used, and I'm fine.
12. I'm ambivalent about "maybe". Sometimes it works, sometimes it doesn't.
13. "stuff" meaning "things". Avoid in formal writing. But: "He is made of sterner stuff" strikes me as acceptable, as is "the right stuff" (though cliched... but I don't generally get worked up about cliches).
14. Meh
15. Here's a place where I am fine saying "never": "never use 'irregardless'".