Suitability for precision will depend entirely on the quality of the unit. (I have no experience of Hawke red dots.). Some of the cheap stuff have big, slightly imprecise dots and dodgy adjustments. Whereas an Aimpoint or EO Tech or similar can shoot 1MOA at 100 metres all day long on a good centrefire rifle.
Unlike the Singlepoint, BSA reflex (a truly poor sight) or the Armson OEG, you don’t need to have both eyes open, but you should - with any and all sights.