Please remember, one wrong click, a browser freeze, a single unexpalined step in the process, many things can cause the steps to go awry.

Following the instructions above only query a constant (read) function that does not write. Nothing bad can happen. If you're referring to calling the register() function, nothing bad can happen either. It's a non-spendable function. You cannot send ether to it, it only accepts a 0 value in the transaction. ERC20 tokens are only sent by using the Transfers function of the corresponding token contract ... EOS ERC20 tokens cannot be sent in any way through a function in crowdsale contract (other that from receiving tokens through claim or claimAll functions.)

These details are absolutely crucial, and I can understand why that guy in a related thread who was using fuck every other word was pissed.

I cannot empathize, that guy isn't confused, he's just angry.

It may seem easy enough to expect users to read between the lines and just "get it" that there's this other drop-down, but it should be made completely unambiguous. And I would fix this in the explanation above.

I apologize that these instructions were not clear enough for you, these MEW instructions are specifically for advanced users familiar with MEW. When I wrote this, I was writing other tutorials as well as spending 12-14 hours a day giving free help in the EOS telegram. Apparently this article accidentally omitted the "this is intended for advanced users" heading I normally gave them. Unfortunately STEEM articles are not editable after 10 days or so, it's a flaw with this platform.

As a sidenote, the screenshot shows the "keys" dropdown which makes it fairly obvious it is not the first dropdown. That said, it could have been more clear.

I still see a zero beside EOS, which leads me to believe that I don't have my own EOS. How would I access them if, for example, I wanted to sell them?

ERC20 tokens are represented by their corresponding token address. Each ethereum client includes a token in their list at their discretion. Try watching a custom token as explained here
https://steemit.com/eos/@sandwich/how-to-transfer-eos-erc20-tokens-using-myetherwallet