How does the continuous/peak charge/discharge current change when combining cells with known values in series / parallel arrangements?
First of all, I don't have real experience with LiFeO4, but I have some basic knowledge about Li-Ion battery. So just want to tell what I think, hope it can be somewhat useful.

Because you connect batteries in series &amp; parallel, it's sure that current can't be simple multipled by spec of a single cell.
Ex: About discharge, I believe that if 1 cell can discharge at 1C, 2 cells in series also can discharge at 1C, 8 cell in a series is the same. But depend on real capacity of the lowest cell, that cell will impact to total voltage (dropped),especially when one cell is empty.
About charge, surely you need to do balance charge, this will make the charge-time longer, so it also mean you can't reach max current charge (1C) on every cell, at everytime. When a cell's voltage lower than the others, it should be charged, other cell need to wait, and vice versa.
For peak charge/discharge, it's truly the same. We know that when peak charge/discharge, cell's voltage will reach its max/min limit. And surely, the worst cell will reach this limit faster than the better cell. So you still can source (discharge) at max current, but the time of discharge (100s) maybe can't reach.
The peak charge is as the above example, balance charge, so you can't apply max peak charge.
About parallel cells, higher voltage series will be discharged first, so when first series will source 1C, second series will source only 0.8C (for example) to reach the same voltage. mean total is 1.8C max.
The real value depends on the difference of cell, can't tell exactly.
I don't know there is an ideal battery chemistry that can reach max powwer when you seri/parrallel them. Should be no, because always exist difference between cell.