Learn Italian: Non possiamo posticipare il progetto, la data è improrogabile. - We cannot postpone the project, the date is strict.

It translates closely to unpostponable or unable to be extended. It is built from the negative prefix in- (which becomes im- before a 'p'), the verb root prorogare (to extend or defer a deadline), and the suffix -abile (able to be).

Could I use rimandare instead of posticipare here?

Yes, rimandare is a very common synonym for to postpone. However, posticipare sounds slightly more formal and professional, which pairs perfectly with an advanced word like improrogabile in a business context.

How could we use this lesson's focus word, altrimenti, with this sentence?

You can use altrimenti (otherwise) to show the negative consequence of postponing. For example, you could connect the ideas by saying: Non possiamo posticipare il progetto, altrimenti non rispetteremo la data improrogabile (We cannot postpone the project, otherwise we will not respect the strict date).

Why are these two clauses separated only by a comma instead of a conjunction?

In Italian, two closely related statements can often sit side-by-side separated only by a comma. The second statement implicitly provides the reason for the first. If you wanted to make the cause explicit, you could replace the comma with perché or poiché (because).