How exactly my eth will be exchanged for the chips there, and my winnings will be credited in eth as well?
At the conversion rate of ETH/GBP, I think Pounds is what the game providers use mostly. But in general you can calcuate as the conversion rate follows.
If you are using 1 unit of a cryptocurrency to deposit and its equivalence is 100 units of a fiat currency then you get a total chip denomination of 100 units fiat.
Also eth price changes all the time, will it influence my balance at FJ?
Straight answer is yes. But lets look into this more carefully. When your chip amount is in play, more or less it is locked or not is not known to me clearly. FJ officials may clarify this too.
Now consider you have 1ETH worth of coins in deposit. Consider market price of ETH drops by 1%. It will not have a huge impact on your money deposited unless you start making whale level deposits. Average market swing if within 2-3%, it is manageable.
Now what to do about this your choice. If you dont like it then dont play with cryptocurrency deposits.