Do inhaled corticosteroids increase susceptibility to fungal/bacterial resp. Infections (besides candida)? Environmental mold, or healthcare exposure?

Not usually. Usually just thrush if you have a normal immune system. Not sure what the second part of your question is asking. Here is some info about on of the inhaled corticosteroids:
Steroid risk. The answer is a qualified yes. But, the increased risk is minimal if they are used as prescribed AND you have no reason to be immune suppressed. If your blood sugar is not well controlled (given your obesity) that also increases the risks overall.