(as in a ponzi scheme, central banking, communism, capitalism, ...)
✔ Yes. It is an incentives scheme invented by Satoshi Nakamoto. No, he didn't invent 'blockchain technology'.
(as in a company, firm, ...)
✔ Yes. It is a group of people driven by a common goal, organized by the Bitcoin incentives system invented by Satoshi Nakamoto. The organization is sometimes referred to as the Bitcoin d.a.o. (decentralized autonomous organization)
✔ Yes. By buying bitcoins you are making an investment in the common Bitcoin enterprise, with an expectation of profit, which predominantly comes from other peoples' efforts. By owning bitcoins you even have voting and dividend rights.
(like paypal, visa, ...)
✔ Yes. The product that the Bitcoin organization offers to its customers is a value transfer service.
✔ Yes. Bitcoin is the native currency of the bitcoin network.
✖ No. It is not common, i.e. producer independent. Only the Bitcoin organization can issue bitcoins and bitcoins only have value as long as this issuing organization remains operational.
✔ Yes. Both BCH and BTC are products of the same organization. Same as Messenger and WhatsApp are both Facebook. Same as Coke Cherry and Coke Zero are both Coca-Cola. It is a common practice for one company to offer multiple competing products. The company does not care much which of the products win in the market, same as the bitcoin miners and pre-split shareholders don't care whether BTC or BCH wins. It is also common for one company to have multiple types of shares after a stock split - see for instance GOOG and GOOGL.