To address the second part:
> and yet the plane appears to have no mechanical backup instruments[?]
This is unlikely in a modern aircraft because mechanical instruments to back up e.g., the artificial horizon / attitude indicator or directional gyro (DG) / heading indicator are:
1) Mechanically complex - the attitude indicator and DG make use of gyroscopes which rotate at up to 24,000 RPM along with other mechanisms. They are typically powered by vacuum or electric motors which consume relatively more power (or require vacuum lines and a vacuum pump)
2) Expensive to maintain - see (1) - they need to be serviced somewhat regularly
(3) Heavier than their solid-state counterparts
(4) Have [dramatically] different failure modes - instead of a display going dark, a DG will slowly drift as the gyroscope precesses, giving erroneous values. Same with the artificial horizon. This can lead to catastrophic results under instrument meteorologicalconditions (IMC) where the pilots rely solely on instruments to maintain essential things such as heading and level flight.
(5) Because of (4) they require additional redundancy to ensure instruments can be cross-checked with one another. This compounds (2) and (3)