So is the 2x BTSX that you need to borrow bitUSD based on the USD price of BTSX or the units?
If BTSX is trading at $.50 each, then I need 4 BTSX to borrow 1 bitUSD?
It is based off of the price of BitsharesX relative to the US dollar, as determined by the free market.
You would only need 1 BTSX in the case of BTSX being worth $0.50, as only 2x collateral is needed (I think) if you wanted to borrow 1 bitUSD. If BTSX falls in price and your collateral can no longer cover your 1bitUSD, then your position is released and you lose your collateral proportional to the amount collateral that is required to cover your position.
Am I right in understanding that with BTS is there is no guarantee that you can redeem 1 BTSX for 1 USD because you do not need to deposit a USD somewhere to create a BTS in the first place?
It is determined by consensus on the free market, by some people going long and some people going short on a specific asset. There is no guarantee, but short of manipulation or some flaw, there is no need for a guarantee. The free market will always even out to the true value of the USD as soon as a large amount of orders are placed on both sides, proper volume is established, and skepticism dies down that bitassets will not work for some reason. Because of those reasons, bitUSD will likely be worth less than US dollar until "market equilibrium" (or consensus) is reached. I expect this to happen eventually, but on the release and in the immediate future after the release, bitUSD will likely be worth less than a real US dollar. That is speculation though...