So, I have finished my first 16P pack. It went better than I thought. I only used spot welding @40A for nickel strips and @60A for the split copper strips. I only need to solder a wire for the positive and a wire for the negative pole of the pack to finish it. And... do it 12 more times of course! :?
You can see the result here:
So, the steps I followed were:
1) Spot weld 16 cells in pairs using 25x7x0.15 mm pure nickel strips
2) Connected pairs of cell pairs in a row by spot welding 1st to 3rd cell on positive end and 2nd to 4th cell on negative (Positive of 2nd and negative of 3rd are covered by electrical tape). Used 40x10x0.1 mm pure copper strips split right in the middle to form two 40x5x0.1 mm parallel strips.
3) Used hot glue to stick the four fours of cells and have one solid pack.
4) Spot weld one small 1cm piece of nickel strip on the positive of the 2nd cell of each row and on the negative of the 3rd cell of each row.
5) On the positive end, I spot weld 2nd cell of row 1 to 2nd cell of row 2 as well as 2nd cell of row 3 to 2nd cell of row 4, using 25x10x0.1 mm copper strips split in half to form two 25x5x0.1 mm strips. Also used the same strips to connect the negatives of the 3rd cell of row 1 to the 3rd of row 2 as well as the 3rd of row 3 to the 3rd of row 4.
6) On the positive end I covered with electrical tape the 3rd row and on the negative end I covered the 2nd row.
7) Spot weld a small 1cm nickel strip piece on the positive end of 2nd cell of row 2 as well as the 2nd cell of row 4. Then, I spot weld a 40x10x0.1 copper strip (split in half again) on top of those cells.
8) Like step 7, I have spot weld a 1cm piece of nickel strip on the negative end of 3rd cell of row 1 as well as the 3rd cell of row 3. Then, I spot weld 40x10x0.1 copper strip (split in half again) on top of those cells.
That's it!

It might have taken me some time to do (And it will take a long time to do it again for 12 more packs), but I am very pleased with the result and myself! I am proud I figured out a way of spot-welding copper using my cheap £100 spot welder!
