Do you have to buy bitcoin unlimited coins with my bitcoin? What will happen in the outcome of a bitcoin unlimited hard-fork?
If a hard fork activation of Bitcoin Unlimited were to occur, both the resulting chains share a common blockchain-history:
BTC : ← 6 ← 7 1 ← 2 ← 3 ← 4 ← 5 <split> BTU : ← 6 ← 7
All the coins that were in your possession before the split now exist on both chains. Once you have moved them to separate addresses on the two chains in order to prevent replay attacks, you'll be able to move them independently by using two different Bitcoin wallets that each interpret one of the chains.
As to other results of the fork, I don't feel like it's appropriate to make predictions at this point, but I would expect significant volatility as some users would move to dump coins from the side that they don't wish to support.