Some men's bathhouses do have co-ed nights example from google and I have read of a number that opened as dedicated co-ed facilities, so you should have some options. They will give you a towel and a set of clothes to wear in the mud room and special sauna. I went to one recently and -wow- awesome. I highly recommend this spa. I'm interested in something similar for straight people - in two ways.
Not exactly an open bathhouse, but there is this chain in the Chicago area, Sybariswhich is more aimed at couples.
Denver Gay Bathhouses Saunas
Where you shower first then relax in the hot tub like pool. Ask Joanne M about Havana Spa. Show reviews that mention. You could start out with a shower, go to the steam room then jump in one of the three different temperature pools. But people talked way more about the baths.
For the second part, if it exists, it probably isn't publicized - so you may need to find a crowd that is into that sort of thing first. But please don't have sex in spas and saunas that aren't set up with that intention. They will give you a towel and a set of clothes to wear in the mud room and special sauna. But I don't know of any places that have communal mixed-sex facilities where you could safely have sex with a male stranger. The better clubs have a separate one for each sex, where clothing's optional.