Do I have the right to sue the landlord because of an oven that caused me burn injury?

You would want to first have you lease read by an attorney to see what it says by way of certain responsibilities and liabilities of the landlord; you would be surprised what kind of things are in a lease especially "between the lines" and with an attorney's legal analysis. But in the likely event that it does not cover a scenario like this, even implicitly, then the chances are slim there would be a good case for liability to the landlord for use of an appliance. Even if your story would say there was no user error or negligence, it would be hard to prove that, as would be any negligence on the part of the landlord. But it could be worth a consult to have an attorney review the lease and otherwise look at any possible legal theories if the lease is silent, especially depending on any other facts/evidence you may have.

Maybe, if the stove was defective and you reported to the landlord. You should send her a bill for your medical injury. I would also send her a written request her to fix or replace the defective stove.