Hey smart investors and forward thinkers, I hope some of you respond.

1. What determines the price of each BTC? Is it purely based on supply and demand...
yes
or is it assessed by dividing each bitcoin available with the market cap?
the market cap is set by the current price multiplied by the amount of coins mined.. not the other way round as you suggest


 Do the exchanges set the price automatically or do the miners set the price themselves? I'm still not clear on how this works.
exchanges are not one person. the price is not set by the owner of the exchange, but by the people that trade on the exchange, these people do include miners, investors, payment gateways selling off, individuals buying in.. the question most people are truly asking is why are people dumb enough to allow themselves to sell bitcoin below 1000. if no one agree's to sell below $1000, the price would not drop below $1000.

2. Say in 100 years when all of us are dead, along with most of the initial bitcoin holders... will all these bitcoins be 'lost' because no one will have access to our private keys? Do you think there will be some sort of problem around this?
sometime in the next 100 years i would have either sold off my millions and retired to some island. or i would have had time to write a will offering instructions how my inheritors can claim my left over bitcoins. in this time the bitcoin would as my first thought suggests, transfered from those retiring, to the next generation of young, aspiring entrepreuners and users, simply through trade between now and 100 years time.

3. Do you think bitcoin will come into play during the next US presidential election? I'm hoping by then even more people will be aware of bitcoin and there will be more debate around it. Whoever has the best policy in favor of bitcoin will have my vote.
well ron paul was bitcoin friendly and that did help him get a few extra votes. but not enough to win. maybe if bitcoin was mainstream and a part of everyones life, then yes it would be part of every candidates agenda to be involved. but in the end all politicians lie. so most people smart enough to be into bitcoins dont really believe or care about politics.. in the end they all turn out to be the same