Is specifying and detailing supplications—such as asking for healing for a specific illness or for a specific number of Hajj and ‘Umrah pilgrimages—considered an transgression in supplication, and how can one know that they have exceeded the bounds of etiquette in supplication and become an transgressor?

Allah commanded His servants to supplicate and promised them a response. It is good to raise all needs to Allah, including naming the specific illness for which healing is sought, as this is permissible both within and outside of prayer. As for the claim that whoever performs Hajj three times will have their body forbidden from the Fire, its authenticity has not been established. Among the transgressions in supplication are asking for a status one cannot attain, seeking assistance in committing sins, or asking for something impossible to achieve. If you doubt whether a supplication is a transgression, it should be abandoned.