Must/should the Haftarah be chanted in Hebrew? Can it be chanted in another language such as English in English-speaking countries, Spanish in Spanish-speaking countries, etc.?
The universal practice in all Orthodox synagogues is to chant the Haftarah in the original Hebrew.
In Talmudic times (see the gemara in Megila 24a), there was a meturgeman (translator) who would translate the Haftara verse-by-verse (or 3 verses by 3 verses) into Aramaic (the spoken language at the time). Since this didn't replace the Hebrew but was in addition to it, we might find there the source to always read the Haftarah in Hebrew up to today.
In addition, as noted by ezra in the comments above, there is no way of chanting the Haftarah in any other language than Hebrew since the traditional musical notes are only known for the Hebrew text.
In conclusion, nothing would prevent someone from reciting in addition the Haftarah in local language, either verse-by-verse, 3 verses-by-3 verses or after the Hebrew reading, but this wouldn't replace the traditional reading.
Of course, CYLOR if you need a practical ruling.
This extremely well-done documentary on the Sephardic Communities of Seattle has Congregation Bikur Holim chanting the Haftorah in Judeo-Spanish in order to preserve liturgical use of the language. Certainly not definitive halacha ("look what they did at this one congregation in the 70's!") but worth taking into consideration nonetheless.
The universal availability for many years of authoritative printed linear and parallel Torah and Haftorah editions has largely obviated the basic translation issue, although much is to be gained in learning why one particular translation was used rather than other possible ones. Although there are many vastly different traditional niggunim (trops) for Haftorah, they all preserve the poetic forms and sentence structure - and hence, the intelligibility - of the text. These simply don't survive translation.