NoSQL is best used as a key-value storage, where the value can be non-tabular or mixed data. As an example, imaging you have a session cookie value identifying a user. That user might have many different groups, roles, claims, etc. If you wanted to store that data in a RDBMS you would likely need a table for every 1-to-many data point (Session -> SessionRole, Session -> SessionGroup, etc). In NoSQL this would be represented as a single key with a json object that could looks quite different from other Session json objects. If you then need to delete that session it's a single key delete, where in the RDBMS you would have to make sure that delete chained to the downstream tables.
This type of key-value lookups are often very fast and used as a caching layer for complex data calculations as well.
The big downside to this is indexing and querying the data not by the primary key. It would be hard to find all users in a specific group as you would need to scan each key-value. It looks like NoSQL has some indexing capabilities now but when I first used it it did not.
Since Stargate is my go-to scifi I'm kinda offended at the "doesn't take itself too seriously". Sure it's not as hard on the science as The Expanse (you know, except for the magic portals to other stars), but it feels like it takes itself pretty seriously. There are obvious bottle episodes that were probably written for other shows and shoe-horned in because they were cheap to buy and produce.
For #2, I think this would get pretty old pretty fast, not to mention that they have to fit everything into runtime constraints. Every new planet the team spends months researching the new language. Sure, you could handwave it (we found a Goa'uld translator just laying around), but that would be back to just one language. Since the Stargate presents an instant transportation rather than the days/months/years of starship travel it would make sense that languages stay fairly consistent as people move from planet to planet.
For #3, they pretty much handwave this in SG-1 as the majority of planets in the Milky Way were repopulated by the ancients in their image, and others were transferred from Earth.