When (if ever) can you read a non-standard haftarah, and how far afield can it go?
Years ago, in a year when US Independence Day fell on Shabbat, I was away at a kallah, a week-long retreat for people from many communities with study, social activities, and, of course, davening. During the torah service on that Shabbat, the people leading the service said that in honor of "yom tov" they were going to do a special haftarah -- and proceeded to chant parts of the Declaration of Independence in haftarah trope. This was tied to a d'var torah about the limitations on kings in torah (comparing the two lists), so it was actually connected to torah in the end. At the time I was amused and struck by the relevance, but I later wondered about the halachic issues involved. (This was not a completely-halachic gathering.)
There are special haftarot throughout the year for days, seasons, even the day before Rosh Chodesh. Replacing the regular weekly reading with another is well-established practice. And the institution of haftarot was, if I understand correctly, as a proxy for torah readings that were at the time banned by hostile governments, and then even when the bans no longer applied the tradition continued. I don't know if, today, they have a lesser degree of obligation than the torah reading, the same obligation, or, strictly speaking, are optional.
When, if ever, is a "new" haftarah reading acceptable?
Only if it is additive -- you read the haftarah you should read, and anything else you do isn't really a haftarah reading but, sure, feel free to read stuff? (Presumably this would be without blessings.)
Only if it is from Tanakh? Other writings or prophets are fine, but secular documents aren't?
Only if it is not done with trop, which could mislead people? (In this case it was English, but it might not always be.)
Never -- haftarah is for the assigned portion, not other stuff, period?