Waste heat in battery pack - large pack vs small pack?
Is there really 780W difference in battery pack waste heat?


Yes, your sums are correct. There is a large difference in internal heating between a 13S2P and a 13S6P, assuming the same load and the same cells.

Look at it in terms of just the battery internal resistance. The 2P pack has about 0.33 ohms, the 6P pack is 0.11 ohms.

At 60A, that gives you an \$I^2R\$ heating of 1188 Watts or 396 Watts.

If you reduce the internal resistance by whatever means (better cells, or more of them in parallel), the battery internal dissipation will fall.


  Does inner battery cell resistance stay constant over different current draws and temperatures?


To some extent. 

We often measure a voltage drop, and a current, take the ratio and call it resistance. This is only useful if that ratio stays fairly constant.

In a cell, there are several contributions to the excess voltage drop, at any given current. Amongst these are several reasonably constant terms like electrode resistance (increases slightly with temperature), less constant things like ion mobility in the electrolyte (changes with temperature, probably reduces), and things you've have no right to expect to be constant like polarisation potentials (the effect of a redistribution of the cell's active chemicals due to current flow, so it has a time history as well).

Whether any of these terms dominates depends on what chemistry and what quality of cell you are studying. The only way to measure the change in terminal voltage as the current changes (the definition of effective internal resistance) is to load the cell with a varying current, and measure the voltage.

When a cell manufacturer makes a claim about the maximum current the cell can deliver, that's an implicit claim about the maximum internal resistance you're likely to see during its operation. You would certainly expect it to deliver that current into a short circuit. You might hope it would deliver that current with only 25%, or maybe only 10%, terminal voltage drop due to internal resistance. 

In all cases you need to read the data sheet, or do your own measurements.