'On' would work in both cases.
'Of' would be wrong in both cases.
For the first gap, you could use 'on', 'about' or 'regarding'. 'Regarding' or 'on' are the best choices, but 'about' would also be OK.
For the second gap, 'on' is the only natural collocation. 'To be an expert on something' is a set phrase. 'About' is less natural, and 'of' is wrong.