They are the only consistent model of reality there is.
No, a field doesn't fill space, space is relative and e.g. the gravitational field defines space-time as per GR. Fields define and make up spacetime
My long standing gripe with causality has always been that it's a secondary(derivative) concept(like matter, space and time). You are looking for the organizing principles where they don't exist.
Memory is a secondary, emergent concept as well(a property of the field?). Classical realism of objects as a fundamental characteristic of reality has been dead for a while.
QFT doesn't pressupose realism, so no problem in that respect with QM.