Do panels often fall from airplanes?

Yup; it happens from time to time. The term of art for these events is “uncontained engine failure”. See Turbine engine failure - Wikipedia for more info and a list of uncontained failure incidents, some of which precipitated crashes and others did not. Here’s one non-crash event with fatalities: Delta Air Lines Flight 1288 - Wikipedia for an example.

The nacelle structure is required to fully contain the loss of a single fan blade. YouTube has many videos of these spectacular tests. There is no assurance that a more severe failure will contain all the parts vs. all the centrifugal forces. Certainly the engine is designed to absorb a lot of typical failure modes. But it’s not proven to absorb all. There’s also the reality that a fan blade coming off has a cascading effect downstream. Any given test of any given engine model provides one data point on how one particular cascade happened to develop. Engineering analysis provides the rest of the simulated expectations about simulated repeated tests. Real failures may not fully conform to the engineer’s work.

These failures, regardless of any human injuries are on the NTSB’s list of Really Big Deals That Must Be Fully Investigated. Precisely because of their high probability for major collateral damage to either the machine or the people.

Late add:

One of the (several) issues presently obstructing development of propfan type engines is deciding how to regulate and manage the threat of blade loss events.

Historically there’s no requirement for failed propeller blades to be contained or containable. There is such a requirement for the fan of a turbofan. What about this hybrid that will have the fairly high RPMs and high blade counts akin to a turbofan but without any sort of containment shroud like a propeller?

No connection. The Qantas A380 was powered by Rolls-Royce; the Air France A380 was powered by Engine Alliance.

EDIT: Perhaps I should say “Exceedingly unlikely that there would be a connection”…