Is #10 wire correct for my mini-split system on a disconnect?

You can use any wire you want, 10 AWG or larger... so if you have some #6 lying around, don't make a run to the store lol.

As far as circuit breaker, 30A is fine. What the label is telling you is that if you get nuisance trips, it's OK to bump to 35A or 40A. Or even 45A, but that is not a commonly made breaker size, so that basically means 40A lol. It might be available in fuses.

Yes, use #10 AWG. The minimum circuit capacity per the manufacturer must be followed. You will also have to replace the 50 Amp breaker with a 30 Amp breaker and pigtail the # 6 AWG to a piece of #10 AWG since the #6 won't fit (probably won't) into a 30 AMP breaker.