The integral G max dt is over the time the phase encoding gradient is turned on. The shape of the phase encoding gradient pulse is immaterial as long as the area under the pulse is appropriate. . When two features in an image are distinguishable, they are said to be resolved. Resolution is a measure of image quality. When two features 1 mm apart are resolvable in an image, the image is said to be a higher resolution image than one where two features are not resolvable.
Resolution is inversely proportional to the distance of two resolvable features.
It is easy to see the relationship between resolution, FOV, and number of data points, N, across an image. You might think that increasing the number of data points across an image would improve resolution. Increasing the number of data points will decrease the pixel size, but not improve the resolution. A magnetic resonance image can be thought of as a convolution of the NMR spectrum of the spins with their spatial concentration map. Here are two images of an infinitely small point source of NMR signal.