It would be bounded by 0 and 1 obviously, so you wouldn't report a value >/< than feasible. Bounded variables within 0 and 1 can fall into the beta distribution.

I am not sure given the process if the SE would be std / sqrt(n-value) , where n-value = 10, as in the case of say bootstrap the std is the SE, I would favor the former if guessing. I have seen the formula somewhere before online.

So 10% was used for model building and then applied to 90% to get AUC, for all 10 data partitions, correct?

If you have random samples from a population the average of the estimate is the expectation for the parameter based on Central Limit Theorem and you seem to do that for the first part of the problem.