I'll try and number these off and take them in order, mostly so I don't miss or confuse anything.
1a. Genestealers were much earlier, taken from fluff in rogue trader and most importantly Space Hulk. They were arguably the biggest 'homage' to Alien and Aliens you'll find in the tyranids (At least until 3rd and 4th edition, that started adding inner jaws, and Xenomorph back spines to nearly every Tyranid model
1b. While the final two pictures are of Tyranid Warriors, who are ~extremely~ popular because they're an inexpensive Synapse creature. The First picture is of a Hive Tyrant, another very popular Tyranid model.
2. Tyrannid armies aren't really limited by Synapse creatures at all, during invasions the majority of the swarm isn't brought under the yoke and simply kills and feeds with wanton abandon on the world. It's only in the face of organized resistance that you'll find Hive Tyrants, Warriors, and Zoanthropes the three most common synapse creatures.
Cerebrates(Later to be replaced by the Queens) and the overlords they use to supplement their will dominate and control all members of their brood at all times. A Zerg not under control of the hive mind is a wild animal, and in fact wild Zerg nest and live of most worlds assumed to have been cleared of infestation.
3. Genestealers are the only member of the Tyranids that infest and infect creatures to control them. You can find a lot of information about this here
http://wh40k.lexicanum.com/wiki/Genestealer.
However, Genestealer infestation only became a thing in 2005, 7 years after the release of Starcraft, were it was covered in the WH40k fluff book Xenology. (Check it out, it's a pretty good read)
4. Tyranids do have a hive mind! Unfortunately it's been a real pain in the ass figuring out just how much of it is Hive, and how much of it is Mind. Tyranid fluff either has them as an almost entirely instinct driven beast that just consumes and reacts, to hyper intelligent alien planner who's tactics are beyond mortal (and in the case of demons) immortal minds. Unfortunately even the Tyranid codex doesn't help.
5. While they do cover worlds in biomass, that biomass has teeth, legs, and wings. Tyranids don't invade a planet for keepsies, there is no creep analogue here, and the two things you'll find on tyranid controlled worlds are Capillary Towers to transport biomass to hive ships, and pools of melted biomass (Into which any remaining Tyranid warrior organisms will be thrown into too) Tyranids, for whatever strange reason can't make more Tyranids without first turning living organisms or deceased organisms into biomass, from which springs all Tyranid life. (They also drain all water from the planet, which considering the Tyranids aren't made of 99.8% water really makes you wonder what they hell they do with it.)
Zerg on the other hand, do cover and terraform a planets surface to be more habitable for Zerg lifeforms. Once the Zerg have dominated a planet it effectively becomes a self sustaining world through which the zerg continue to produce more Zerg to invade another world to start the process over again. Think Space Cancer, but with teeth.
6. While you're right in that both names have Dark in them, I think that's where the similarities end.
Dark Eldar were perfect for what they were, which was Dark Elves thrown into their WH40k universe. Eldar have always been space elves, and unfortunately from them, changed the least with the carry over to the new Games Workshop IP.
Sorry if I missed anything, I had to pull out a few old 'Nid Rulebooks and my old Starcraft manual to clarify a few things.