Backdoors being engineered into stock hardware is unlikely. A large number of people would have to be involved in this engineering process, and all of them would have to stay quiet about it. This does not seem realistically feasible to me.
I'm not sure. It depends on how it's done. Poisoning the intended schematics would probably be discovered, although I'm not entirely convinced by that, but It seems it would be almost trivial to introduce hardware MITM components which would be invisible and go unnoticed by most people in the fabrication process.
Yes, but it's not about going unnoticed by most people. For a thing like that to stay quiet, it would have to be unnoticed by all people involved. This seems probabilistically very unlikely to me as the number of people involved in the process grows...
In the last year we did see Linux on HD controllers and SD cards, so I do not think that they need to be backdoored by default, but a exploitable keyboard controller seems to be possible.