@JamesRisner (1) I assume you mean API key? You should virtually always create an API key for any app/script that you're developing. Otherwise, you're going to be working solely off of the rate limit for your IP address, which is extremely low and very easy to exhaust if you're doing much at all. There's virtually no drawback to registering an API key. You can read more here.

@JamesRisner (2) You almost always want to run a bot under a dedicated account, unless you have absolutely no choice. Why? Principle of limited privilege. Same reason you don't log in as "root" on your Linux machine to browse the web. You are responsible for anything done with your SO/SE account. Mods don't care that it was a bot gone rogue; you're still going to be held accountable for any actions taken by your account. That's still true for a dedicated bot account, of course, but since that account has limited privileges, it's a lot less likely that it will cause any damage. Worst case, the bot account creates a disruption and gets a short suspension, long enough for you to explain to a mod what went wrong and get the issue resolved on your side.

So, that's what you should do if you're going to monitor chat rooms for replies to you, as you don't need any special privileges to do that. On the other hand, if the bot needs access to your account's global SE inbox (the red notifications in the top bar), then it will need to run under your account, as only your account has access to your account's notifications.

For questions about API usage, API keys, etc. (e.g., #1), those can be asked on Stack Apps.

For questions about etiquette of running bots (e.g., #2), that probably belongs on Meta Stack Exchange. (Although it is probably already discussed there.)

I don't think #3 really can go on a Q&A site, but that's a simple enough question that it can be asked and answered here in chat or whereever.

for #1 see also: stackapps.com/questions/8971/i-only-need-a-key-what-do-i-do and and stackapps.com/questions/9224/… if you only plan on using Chat / Chat websocket, then there is no key needed as that "API" isn't official.

do know chat has its own section in the rate limiting guide: meta.stackexchange.com/questions/164899/…