I can't report this as an error because it's just being classified as a typo, but I answered "Dozvědela jsem se..." and they marked it as a typo. It should be accepted as correct.
I think Dozvědela should be Dozvěděla.
What about "Zjistil jsem, že František umřel"?
I am not a 100% sure, but I think that'd mean you felt his pulse and declared him dead.
Not necessarily. zjistil jsem = I found out