By using the EPT run design command, are the previously designed elements removed?

Yes, they are but only the first time the command is launched as - for future design phases - the existing packs need to keep the same slotting.

It depends, the user is prompted to choose whether to delete or leave the previously designed elements.

Not the design is always progressive, on top of the previous design.

Yes, although this is not happening in case of GMPLS-enabled nodes because existing slots cannot change as they are controlled by another manager (GMRE).