Yes they do.
The past participle of "get" is "got" in British English and "gotten" in American English.
The past participle of "get up" is "gotten up" in American English and "got up" in British English.
The past participle of "burn" is "burned" in American English and "burnt" in British English.
The past participle of "focus" is "focused" in American English and "focussed" in British English.
The past participle of "sneak" is "snuck" in American English. In British English, the past participle can also be "sneaked."
The past participle form of "get" is "gotten" in American English and "got" in British English.
The past participle of "signal" is "signaled" or "signalled" (in British English).
The past participle of "spell" is "spelled" in American English, and "spelt" in British English.
The past participle of "spit" is "spat" in UK English and "spit" in US English.
The past participle of "learn" is "learned" in American English, or "learnt" in British English.
The simple past tense is got. The past participle is generally got in British English and gotten in American English.
The past participle of "avoir" in French is "eu," which means "had" in English.