It doesn't need to be convertible to cash to have economic value. As long as people are willing to trade bitcoins for other goods, they have value. So even if it could never be converted to another currency, that wouldn't necessarily mean it's useless.
Are you sure? At some point someone along the line needs to convert it to currency. The only time that wouldn’t be true is if there was a big enough marketplace that anything you might ever want can be purchased in Bitcoin. Otherwise you’d need some way to convert to currency to access other goods and services.
Of course. Currency itself only has value due to its ability to be traded for other objects. Currency on its own has no value. Bitcoins are in the same boat. If bitcoins can be traded for other objects, they have value regardless of any ability to trade them for currency. Put another way, the only thing that bitcoins (and dollars for that matter) require are that people perceive them to have value.
Besides even if bitcoins cannot be directly traded for dollars on an exchange, the same could still occur with intermediate objects. If I give you bitcoins in exchange for a laptop, I can then turn around and sell that laptop for money. It's not as convenient (and could be illegal), but it would work.
