regarding the origins of patch..

I'd surmise that all of that confusion stems from what James Murray and Co. found:

[ME. pacche, patche, of unascertained origin. If native, its OE. form would be *pæcce.
Some have conjectured an earlier *platche, with subsequent loss of l, comparing mod.Sc. PLATCH, q.v., but for this there is no evidence. Ger. dial. patsche puddle, mire, ‘mess’, also instrument of striking, hand, patschen to splash, dabble, dash, clap, tap, suits the form but not the sense.]