Theoretically, no you can't as your working visa is linked to your job place and to the institutions or company who filed the request for your visa.

You can however try to work under radar, but with the risks that go with it.

If the company is under once license that is a franchise or has more than one office, yes, but you are still restricted to the city your resident visa is on, unless you travel for your company and your resident visa would state that also. 

it think it depend on the second job, if you are free lance for the second one like a consultant or Tutor i think you can do it. but if you mean work at two different offices then it would be vary hard, even if you could get the government to approve.

PS there might be exceptions so list full detail.

Yes according to the Chinese L law. If you need more info feel free to contact me with your questions directly under logan5680@hotmail.de

Greetings from Beijing and Chengdu

Legally yes! Some companies make it mandatory for you to at least tell them you are gonna work for another company. Some companies ask you to let them know but many foreigners and other employees don't abide by the law sometimes! 

maybe part time is ok, if fully time, i think in any country it is not acceptable, 

legally no. so keep your mouth shut even if your employer says yes your visa ties you to one company only but it is commonly un enforced

normally, it is impossible for you to set up labor relation with two companies or maybe banned by employer. however if you do technical job such as research work, it is possible to work in two companies with labor relation.