Black bits are algae, harmless but undesirable.
Caravans need their fresh water systems purging with Puriclean, Milton or other chlorine-based cleaners at least once a year, more often for heavily used caravans.
Drain the system down completely, including any on-board and hot-water tanks - remove any filter elements - fill the system with a solution of Puriclean, Milton, etc - allow it to stand for an hour - flush all remaining solution through the system - drain down - refill with fresh water - flush through - drain down - fit new filter elements.