1) How to get a business visa to China?
You need an invitation from a company registered in China justifying the purpose of your visit, take the invitation to the embassy in your resident country along with your passport.
Depending on the situation and your nationality, the embassy/consulate might ask for more documents from the inviting company like: Business license, export record, and more supportive documents.
2) Can I get a business visa from company A in City A and go and visit City B?
but it's common, however, it's getting strict recently.
If you got caught beyond your visit purpose, both you and the inviting company have to bear the consequences including: Fines - deportation - blacklisting the inviting company from inviting any foreigners in the future.
3) What's the duration and terms for tourist or business visa?
Duration and exit terms (e.g. 30 or 60 days), etc are determined by the officer at the consulate/embassy based on different factors mainly related to the content of your invitation letter.
Business visas are meant for business purposes such as factory visits, conferences, meetings and similar affairs and not for working.