- Yes. It's called the "out-of-africa" theory. It's a paleoanthropological hypothesis with substantial support from genetics, in particular studies on mitochondrial DNA. Much work has been done by Luigi Luca Cavalli-Sforza and others. See his book Genes, Peoples, and Languages. The linguist Merritt Ruhlen is one of the most important linguists to test Cavalli-Sforza's hypothesis, see the Santa Fe Institute website.
- No. But language superfamilies remain a problem.
- All the links provided above are relevant. A further term is diversity (but try to google more, the Wikipedia section is not that illuminating), see also language families.
Concerning your specific assumption that isolated bands leaving Africa contribute to the founding of distinct language families, is, however, problematic. Diversity studies comparing African vs. non-African languages consistently show that the two major African language families Niger-Congo and Nilo-Saharan are much more diverse among themselves than all other non-African language families combined. (That, by the way, is also consistent with genetic diversity: there's more genetic diversity within Africa, than in the rest of the world combined.)
This can either mean that many bands leaving Africa have not contributed to the current "gene-pool" of language(s), or it can mean that there weren't that many bands to begin with.
Personally, I believe that the latter is the more compelling assumption because it matches what is known from studies on mitochondrial DNA. See this picture, which shows that only group L3 left Africa. This group may have been diverse, and surely consisted of different bands over a certain time span, but their genetic proximity suggests cultural proximity, and hence linguistic proximity. The assumption that members of this group used mutually incomprehensible languages is far-fetched, given that these bands weren't that large to begin with.
I hope that helps.