1A. (As you have 2 number one questions.) Do you mean the cartridge itself? Probably a while I would assume as with any good game cartridge or disc. As for the shaking thing, but I'm going to go with a resounding no.

1B. Yes it is, and yes it's a sequel, but it's a sequel in the Final Fantasy sense which is that it has nothing to do with the ones before except brings about some common themes and symbols (i.e. Summons, moogles, spells, abilities, etc.) And they knew Cid because he is the foremost authority on airships and world famous as an airship creator. Besides he's just Cid, everyone knows him just like Unne.

2. Their entirely different, especially since FFIII was originally an NES release where as the FF'III' that appeared on SNES was nothing more a renamed FFVI but Square thought us Americans to be too dumb and would be too frightened at the idea that they never released FF II, III, or V, so they just changed it's name. As for how close it is, it's a lot different yet the same. They made actual characters and dialogue where as the original NES version featured little dialogue (among the main characters at least) and the main characters you start with all at once as their 4 orphan boys (brothers if I recall) with no set names.

3. I dunno I have yet to purchase a DS so I'll wait for someone with more experience on the matter to answer for you.