Learn English – a person with no lower limbs called

Prerequisite - Co-requisite - Post-requisite -- Where task A is the prerequisite and task B can either be a co-requisite or post-requisite.

As a project manager I have often used predecessor/successor, but usually where there is a chronological order.

Project tasks are related in exactly the same way that some educational courses are. This does imply providing some sort of utility, but not necessarily and the relationship is well understood.

With this in mind, one of my college chem classes was a prerequisite and an associated chem lab was a co-requisite.

I don't know of any specific terms for the person or the cancelled leave, but I wonder whether your colleague might have said "bump", not "pump".

I could understand someone referring to the leave being bumped, i.e. moved to a new position (date). (See definitions in The Free Dictionary).

The alternative day off may also be referred to (at least in the UK) as a "day off in lieu", i.e. as a day off instead of the public holiday. (See definition in Oxford Dictionary Online.) In fact, in the UK you will sometimes be entitled to two alternative days off if you were required to work on a public holiday.