One analysis of uniform linear array for different scanning angle I am attaching here. It is a mathematical model for FNBW to illustrate it. It may help you regarding the first query.

For the second query, I can assure you it is the periodicity of the array factor that produces the image beam (grating lobe), and this periodicity for uniform linear and planar array is majorly controlled by the spacing of elements and direction of target only. A broadside linear or planar array suffers from the back lobe as linear arrays produce omnidirectional pattern in elevation plane, and for planar arrays (geometry assumed in x-y plane) sin(pi-x)=sin(x). Whereas endfire arrays have no such problems (for planar arrays x=pi/2). An endfire linear array with half wavelength separation of element produces a grating lobe as sin(2*pi*lambda/2)=sin(pi)=0.