Can I go swimming with a perforated eardrum?

Yes, but. It is a good idea to protect your ear from water with a silicone ear plug that molds to your outer ear. Best to not use plugs that fill the canal. If you feel as if water gets into your ear then the use of an antibiotic ear drop can help prevent infection. You should speak to your ENT doctor about these drops. If you have not seen an ENT recently you should as perforations need to checked.
No, unless.. Unless you have a perfect way to seal the ear canal, no -- very bad idea. If you saw MD for this you should be on drops and should have strict instructions for activity. Do not take a chance on worsening this situation. Good Luck -- be wise.
Be cautious. I think the safest thing would be to protect that middle ear from water exposure and this can easily be done with an ear plug.
Not recommended. The best is go to visit an ENT, follow his/her instructions on staying out of pool and being careful in shower. Good luck!