1. Yes, it means "I have to leave". 2. Kayla has already correctly answered this regarding the US. "I gotta jam" and "I gotta split" I think are slangs from even before the 90s. I suppose that the danger with slang is that it can quite quickly become outdated :)

I am from South Africa. This is slag for-"I got to go" most common with the youth. It seems to be a growing trend amongst the youth in my country.

I am from the US. I have never heard or seen "I gotta jam" (= "I have to jam") to mean "I have to leave"/"I gotta leave". It's possible that a particular community or group of native speakers uses this expression as local slang or in-group slang, but so far it is not used by most people who are not part of that particular community or group.

Im from Northern Ireland in the British isles. How i would say this informally would be "I got to go" although "I gotta go" is more natural.

Thank you!