Full Question
1. When one Chinese company sells to another in China, is the VAT paid directly to government or to the selling company?
2. When I get quotation ex factory, does that include 17% vat?

Answer
You asked:

"When one Chinese company sells to another, is the VAT paid directly to government or to the selling company?"

The selling company is responsible for paying the VAT to the government rather than the buyer sending money to government. If the VAT has been paid on the transaction, then the seller should be able to provide you a formal receipt "fapiao" showing taxes have been paid. If the buyer is planning to export the product out of China, it is important to get those "tax paid receipts" because the exporter will need to show them to the tax authority in order to get any potential VAT rebate upon exportation.

You asked:

"When I get quotation ex factory, does that include 17% vat?"

When buying in China, the quotes are often come back to you in one of three ways:

1. ExW: Also known as "Ex-Works", "Ex-Factory" means ownership of goods transfers to the buyer at the factory's door. This price does not include any taxes or shipping. The buyer or their representatives need to organize customs clearance out of China. In practice, there are third parties that will organize export of goods "without tax paid" by charging a onetime "processing fee" which is usually a few hundred US dollars per container. So for small, one-off orders, it may be possible to buy at the ExW level. But we highly recommend that to be safe you base your long-term budgeting on the FOB pricing.
2. FOB China Port : FOB (freight on board) means the ownership of goods takes place after the items have cleared outbound Chinese customs and are on the boat, ready to ship from a designated port (for example, "FOB Shenzhen"). For new-to-China buyers, FOB is a much easier way to purchase than ExW, as the supplier is responsible for handling any VAT issues.
3. ExW with Tax Receipt: means that the buyer or his representatives will need to organize the VAT rebate & customs clearance out of China on their own. This is not an easy task and not recommended for new to China buyers unless they have a trusted advisor that can walk them through the process.

Hope the information is helpful to you.