Is there a strict chronological order that determines the shape of galaxies? Assuming no collision happens, do all elliptical galaxies eventually become spiral? Also, when a galaxy becomes spiral or barred spiral, can it switch between these shapes or is it set forever?
Galaxies evolve from spiral to elliptical.  The spirals are formed by patterns of new star formation in the disk surrounding the bulge, which contains mostly old stars.

As galaxies run out of hydrogen gas clouds, which is the raw material from which stars are formed, then no new stars form, and with no new star formation, the complex structures of the arms are lost. Elliptical galaxies are made of old stars and have little new star formations. They were formed when spiral galaxies merged, causing a burst of star formation, and leaving a bulge of old stars and little gas to make new ones. The ultimate fate of the milky way and the andromeda galaxy is to merge and form a giant elliptical galaxy.