Does a second 'Umrah suffice for a first 'Umrah, concerning which the questioner doubted the validity of his ṭawāf due to the possibility of madhī (prostatic fluid) discharge, knowing that purity is a condition for ṭawāf? And what are the consequences if the first 'Umrah was invalid and he unknowingly committed prohibitions of ihrām, including masturbation?

The emission of madhiy (pre-seminal fluid) necessitates ablution (wudu’), not a full ritual bath (ghusl (definition)). Doubt about its emission does not necessitate anything. The default is that ritual purity is valid until one is certain that it has been nullified. Ablution is not nullified by doubt. Therefore, your first ‘Umrah (definition) is valid. You incur sin by thehibited act of masturbation.