The tub has a lot of play in it what could that be?
You will need to check to make sure that the hub nut is tight and that the bolts holding the bottom plate of the tub in are tight.
Does the split ring support and rub against the inner tub and does it need lubricating like the tub bearing?
Answer WV, No, Do Not lubricate the split ring WH02X10265 but make sure the "hub washer" WH2X1199 is in place first(under the split ring) so it seals properly. You do have the right idea, the split ring does support the tub/hub assembly, and as you tighten the hub nut, all three components compress together in order to drive the tub. Thanks