Re-occurring balanitis: what tests can be done to find exactly what possible type of candidiasis this is? what are all the possibilities it could be?

Balanitis: The question isn't really subtyping the fungal organisms as most are sensitive to topical antifungal such as nystatin. The real issue is why you particularly are getting recurring fungal infections. Diabetics, particularly the uncircumcised, tend to get recurring fungal balanoposthitis. Perhaps a circumcision is in order if you are uncircumcised. See your physician for diabetes testing as well.

No need for...: What you're trying to do is to search its precipitating factors, not its underlying ones. Without modifying or correcting its underlying factors such as regular cleaning ; drying foreskin/glans, especially after each voiding and sex, local use of antifungal/antibacterial steroid cream will not help in the long run, but breed more resistant microorganisms.