Hard fork the longer chain wins but the older clients could choose to keep their chain if they want to. The fork with the most users is the fork that has value, that's democracy.
Not at all. Hard fork means that the chain is now two independent chains. On each of these two independent chains, there is consensus. There's no interaction any more between the two chains, they are now two different crypto currencies. The market cap of the original chain will now be split over both prongs. Of course, users and miners might all flock to one of the chains, and abandon the other one. Or not. In the end, the users will decide upon the market cap split, and the miners will follow.
If one of the Forks is very weak compared to the other, a small group that could 51% dominate the weaker fork , might rewrite a little of the enemy fork's history to completely destroy it in the eyes of investors. A rewrite of say 3 or 4 hours would be more than enough Bad PR to crush its price permanently.
Yes. However, what does this mean ? There are two possibilities:
Initially, there was a HUGE consensus amongst miners to apply the HF. This is why only a small flock of miners continued on the old chain. Otherwise, there is no "weak chain". This can, or cannot, agree with the user preferences.
1) If ALSO the users have HUGE consensus for the HF, then there's only a very small minority of the users not in agreement with the HF, and the non-forked chain being attacked, dying and so on is not harming most of the consensus.
2) If the users are much more divided, say 40%-60%, then, as a miner, you would be an idiot to WASTE your mining hash rate on attacking the chain *where a lot of money is to be made*. Indeed, if a small minority of miners went to the old chain, and you are a miner, instead of WASTING your hash rate on attacking it, you better JOIN THEM and get a lot of rewards. If the users decide to allocate 40% of the market cap to the coins you're reaping in right now with the small minority of miners, that's much more profitable than wasting your hash rate to kill it.
Note, that's EXACTLY what happened to ETC, and that chinese guy, what's his name, claiming he would destroy ETC with his hash power... only to join ETC mining soon.
Because mining a chain with a smaller amount of miners than its market cap is very profitable.