A profitmaximizing competitive firm that is making positive profits

in long-run equilibrium (may/may not) have a technology withconstant returns to scale.

Yes, a profit-maximizing competitive firm that is making positive profits in long-run equilibrium can have a technology with constant returns to scale. Constant returns to scale means that the output of the firm increases proportionally with the inputs, and this does not necessarily mean that the firm is making zero profits. In fact, a firm with constant returns to scale can still make positive profits in the long run if the price of the good it produces is greater than the average cost of production.

Yup