Is it possible for a company to have a positive cash flow from operations in the same year that it has a net loss or to have a negative cash flow from operations in the same year that it has a profit?

Yes, it is possible.

Is it possible for a company to have a positive cash flow in the same year it has a net lost?

Yes, there are three componenets to the cash flow, remember.

1. Operations (which takes into account Net Income/Loss)
2. Investing
3. Financing

A company with high net losses yet a positive cash flow are likely financed completely and are a tell-all sign to investors that this company is either in the early stages of development or has a very weak future.