The problem with Z axis is most likely either inconsistent extrusion or the printed PLA getting pulled alongside the nozzle. Have you tried lowering the temperature (the printed PLA getting dragged along and oozing are both present), adjusting the Z offset (though unlikely to be the sole problem since your printer should not be stringing this much even if Z offset is slightly wrong), drying the filament (could be responsible for inconsistency of extrusion though unlikely), applying some glue (to improve adhesion if the model is moving slightly when printing), and cleaning the nozzle (some foreign particle is interfering with extrusion) and the sheet (in case bad adhesion)?
The problem with Z axis is most likely either inconsistent extrusion or the printed PLA getting pulled alongside the nozzle. Have you tried lowering the temperature (the printed PLA getting dragged along and oozing are both present), adjusting the Z offset (though unlikely to be the sole problem since your printer should not be stringing this much even if Z offset is slightly wrong), drying the filament (could be responsible for inconsistency of extrusion though unlikely), applying some glue (to improve adhesion if the model is moving slightly when printing), and cleaning the nozzle (some foreign particle is interfering with extrusion) and the sheet (in case bad adhesion)?