ULS is the same as the MINRES method described in Harman's factor analysis book. The equivalence is pointed out e.g. by Joreskog (2007) in the book Factor Analysis at 100. Principal-factoring is an older and different method.
I would use ULS or ML with Geomin rotation in Mplus.
No, I would not hesitate to use ML also for non-normal continuous outcomes. The sample correlations are the same as for ULS and the ML fitting function is more thorough in getting Sigma-hat close to R so estimates will be ok. MLR (or MLM) provides non-normality corrected chi-square and SEs.
Only if the non-normality amounts to floor or ceiling effects would I switch away from the usual approach (ML or ULS) and consider the outcomes as say censored.