Motor current has basically nothing to do with battery current. If you mean you plan to limit yourself to 60 battery amps per side, then no, two 0.2x18mm strips is not sufficient for that.
two 0.2x18mm strips would be good for ~100A at most, and I probably wouldn’t push them past 70 or so myself.
It would be significantly less hassle to just get some 0.15 or 0.2x30mm strip and do it all in one go rather than having to weld three strips for each end of each group.
Not with proper pack design.
Yes, if it’s wide enough. It’s all about cross sectional area. Doesn’t matter if it’s 1mm thick and 10mm wide, or 0.1mm thick and 100mm wide, either will have the same cross sectional area. If you’ve got the width for it (and you do, with 4 cells side by side you have over 80mm of width to work on) I might even suggest going down to 0.15mm thick strip because it’s easier to bend and weld.