Your first problem would most likely be caused by the crank not being properly tightened on the bottom bracket, and it managed to work its way loose. Depending on how significant this problem was, it may have damaged the splines on either the bottom bracket or crankset. I would have expected them to replace the crankset and bottom bracket. Clear case of assembly error.
The second problem, ehh dunno what happened there, chainrings are pretty tough and it takes a lot to bend one. It may have happened the other way around: the chain jammed, then pedal pressure applied a force on the chain in a strange direction that managed to bend a chainring tooth?
Is the middle ring actually bent, or is that what you suspect because the chain managed to derail off both rings? If the latter, chain derailments just happen from time to time, and is a sign that the derailleur tension/limit adjustments need some tweaking.
The second problem is a little less obvious.. error in shifter operation can cause the chain to derail and jam, however it can also potentially happen with a new drivetrain whose shift cables have undergone a significant amount of initial stretch without being readjusted. (The cables only stretch a certain amount though; once readjusted it should keep its tension for the life of the cable) It may have also occurred due to a 'stiff link' in the chain, or some other chain fault that caused it not to track on the chainring properly.
Usually these sorts of faults are fairly obvious in riding: when the cables go through initial stretch, shifting performance will go down the toilet; and a chain with a stiff link will rattle and clatter every time the stuck link goes through any tight bends (e.g. rear derailleur)
With regard to shifting; most shift errors and unintentional derailments occur when you're acting against the spring of the derailleur. (When using the large lower paddle.) These errors can be minimised by pressing and holding the paddle, keeping force on the cable, until the shift completes.
When shifting the 'other way', the spring in the derailleur provides the force necessary to perform the shift, so it's a quick tap-tap type operation.