What should I expect in that period? Will the usual tourist attractions and shops be open between Holy Friday - Easter Sunday? Is there some kind of public tradition / procession that I could participate in as a tourist?
According to This is Chile:
The capital empties out over the long weekend. Typically traffic-clogged streets turn quiet, the air is clear and this bustling metropolis becomes peaceful – making it the perfect time to get out and explore the city.
But they mostly mention visiting churches and participating in masses.