Is the smartphone market a monopolistic competition?

Oligopoly. A few suppliers. Since the phones are differentiated this is a differentiated oligopoly (the phones have different features). Monopolistic competition is where there are a very large number of suppliers. If there were over a thousand companies making smart phones, you would have monopolistic competition.

It's oligopoly. Small number of firms who are well aware of each other and anticipate each other's moves.

yes, I believe it is neither monopolistic and not oligopoly. "Entry and exit: Barriers to entry are high.[2] The most important barriers are economies of scale, patents, access to expensive and complex technology, and strategic actions by incumbent firms designed to discourage or destroy nascent firms.[3]"

There are more than a handful of smartphone makers.

Profit for monopolistic competition is zero ( econ profits that is)

I would say neither.