Is studying a ventilation project for the Grand Egyptian Museum considered Haram, and does it entail sin? And is it permissible to dispose of the money earned from this project by spending it on charitable causes?

It is impermissible to work in these museums, and giving charity from such earnings does not make this work permissible. This is because giving charity from ill-gotten wealth is for the purpose of ridding oneself of it, not with the intention of engaging in such work from the outset.