it's my understanding that miners can decide to mine transactions that include an arbitrarily set minimum fee.
if/when the block becomes saturated, will time/fee amount be calculable?
Is it calculable now? I.e. at x transactions /second, then x fee would give y% probability to be included in next blocck.
There was a good thread posted here about calling transaction fees
bids as that's more accurate. How can you call something a fee when you can set it at any value or disregard it altogether?
To understand how mining and the block chain works think of the lottery. There is simply no way to know who will win the next draw. However, the winner of a particular draw/block gets certain privileges including a reward of funds/coins and the ability to dictate which transactions are included in the block they win.
If they are the winner, then they can include transactions they want, whether the fee is large, small, or not there at all.
By including a fee (or bid if you like) you increase the chance the next block found will acknowledge your transaction, since presumably most people mining blocks are motivated by profits. The higher the bid or fee, the higher the probability your transaction gets included.
Right now, because Bitcoin is still fairly small and it doesn't really cost miners anything extra, many or most miners will include transactions regardless of attached fees, as the goodwill helps Bitcoin overall. The only drawback or limitation to this is if someone is looking to bloat the block chain with valueless spam by sending very small coin amounts to themselves or other addresses over and over since it costs them practically nothing to do this. To guard against this very small coin amounts do require a fee for miners to acknowledge it, or it may not be included into the block chain for a very long time, perhaps many days or weeks. There was a thread explaining the ratio of transaction amount to fee size for likelihood of being included in a block around here explained by DeathAndTaxes who is good with details like that if you're interested.