Are 'First in First Out' (FIFO) system orders allowed?

Mathematically speaking it doesn't matter whether you use FIFO or not... your results are exactly the same, assuming you include open positions in your profit calculations and you mark them to market (as all first-world accounting standards require). 

That said, C2 doesn't allow "hedging" -- that is, having multiple positions open on the same instrument -- one long, one short. You can certainly add to or decrease your position size (which is mathematically equivalent).