Have a look at Chisel infills there are very strength optimised, limitation is currently that they must be single line width, but multiple-lines thick infill will be supported soon.
After that, it's very simple, basically setting double corrugated infill with corrugation size 1 for your rectangle model.
Yes you can!
To have stronger prints you would have to choose the correct direction of filament deposition paths/traces. This answer demonstrates changing the direction of the filament path in Ultimaker Cura slicer.
To do this, it requires some tinkering of your model and choosing the correct slicer parameters (decimals aren't allowed in changing the ...
If on even layers, the routing is in one direction and on odd layers, the routing is the opposite diagonal, you'll have a much weaker structure, as there will be no material after the crossing point.
Addressing that aspect, one could consider that the design is implemented in such a way that the nozzle creates the odd layer continuously from one corner to ...