What is minimum distance between microstrip patches?

If the antennas are phased the combined gain of the antennas is maximum when the distance is λ/2.
If the antennas are not phased and to avoid the antennas to couple one to each other, the distance theoretically should be greater than λ/4.

You can put then very close together (with the smallest separation), but what do you actually want to achieve?
-maximum gain given a minimum number of patches?
-Relative clean pattern (with or without feed taper)?

When you place them very close together (for example using high dielectric substrate), you will have large interaction and increased design complexity. The gain given the number of elements will be relatively low.

Now I read book about radar systems, it says that for monopulse system for -90...90 deg angular position antenna spacing must be λ/2. So i wonder how it looks like for microstrip patches...

For a broadside array (radiation perpendicular to structure, such as a flat panel array), the spacing can be more then λ/2. When you approach or exceed λ spacing for a broadside array, grating lobes do appear (the same phenomenon as happens when undersampling in A/D conversion or optical gratings ).

If you use a beam steering array that can steer over a large range (so that it may become an almost end-fire array), the spacing should be below λ/2 to avoid grating lobes. In other words a broad side array can have larger spacing then an end-fire array.

Distances should be calculated using free space wavelength (assuming that your antenna is operating in air).