Fallout 4 on PS4. I cannot seem to cure Molerat disease, even though I've been to the doctor. Is there anything like Addictol that I can craft to cure all diseases?
It is not possible to cure Molerat disease in normal game play. At the end of the quest in Vault 81, if you have contracted Molerat disease, you are offered the choice of curing yourself or curing August Engil of the disease with the only available cure. If you decide to cure him of the disease, you are granted a place to live in Vault 81, and he survives. More on the specifics of the disease can be found on the wiki here.
As to your second question, the only 'cure all' for diseases can only be found in Survival Mode, Antibiotics. However, this will not cure Molerat disease, as the only possible way to remove it after the quest has been completed is by using console hacks or mods.