Is filing I-539 the easiest way to extend your stay at this time?
Yes. It is also the most difficult way. It is the only way.
Seriously, there could be some kind of amnesty or other program that is offered to non-immigrants in the U.S. who are affected by the pandemic. In that case, you could save a few hundred dollars.
But I wouldn't expect it. I have certainly heard no mention of it, and the current government is deeply against immigrants, so it is unlikely that this will happen without political pressure.
With regard to the risk analysis, the registration fee is well invested.
If so, is it possible to waive the fee due to the corona virus situation?
Applying for exemption will make her look like someone with financial problems, which will negatively affect her application as well as future applications for admission to the United States. I would not do it.
After submitting I-539, should she wait for approval to continue her stay? Or is the receipt good enough?
Once the application has been submitted, it can remain until it is rejected or, if granted, until the end of the extended stay granted.