Print parts fail mid-print
Your printer basically has 2 problems;


stringing, and
layer shifting


The second problem is most probably the result of the first issue. Excessive stringing leads to a lot of material outside the print object, when this clutters, the nozzle could get caught up and cause hindering of movement of a certain axis to result in a shifted layer print as the printer is not aware of this shift, it will continue the print from the shifted reference point.

From your second experiment you see that a larger layer height does not show excessive stringing and the print has therefore not been hindered by caught-up material to finish the product without layer shifting.

It is key to solve the stringing issue; stringing is the result of filament being extruded by pressure build-up in the nozzle that "leaks" out of the nozzle on travel movement of the print head. You will probably not see this happening when you print a single product; it is typically seen when printing multiple objects on the build plate. This usually implies that the printer need to be properly tuned. It is up to you to find the correct settings; test print objects, like calibration prints, help you find these correct settings.

Important print parameters to fight stringing are:


retraction, (do you retract enough prior to movement?)
coasting, (do you stop in time with extruding to make use of the overpressure in the nozzle?)
travel speed, (do you move fast enough to minimize the amount of filament leaking out?)
print temperature, (do you print at a temperature where the filament doesn't get too fluid?)
print part cooling, (do you have sufficient cooling?)


Once you optimized this, the stringing should be gone and the change of layer shifting should have reduced.