It is not permissible to give fidyah instead of performing qaza for a person who has the ability to perform qaza, even if they fall ill temporarily. The ruling for fidyah is only applicable to a person who is completely incapable of performing qaza (due to bad health) and is unlikely to regain their health in the future.
Therefore, in the situation described above, if the lady is not ill (as it appears from the question), she must perform qaza for all the missed fasts because it is not permissible for her to give fidyah instead of performing qaza in her current health condition. However, if in the future, she becomes unable to fast and it seems unlikely that she will regain her health, it would then be permissible for her to give fidyah. Even in this scenario, if she somehow regains her health and the ability to fast, it will become obligatory for her to perform qaza for the missed fasts.
The amount for fidyah is the same as the amount for Sadqa Al Fitr (1.75 kg of wheat or money equivalent to the price of 1.75 kg of wheat). For the fulfilment of fidyah, this amount is to be given to a person who is eligible to receive zakat.