Learn French: Ce projet est moins coûteux qu'il n'imaginait. - This project is less costly than he imagined.

This is the ne explétif, a special word used in formal or careful French after comparisons of inequality (like moins... que or plus... que). It doesn't make the sentence negative at all! It simply emphasizes the gap between reality and what he thought. In casual spoken French, it is usually dropped: qu'il imaginait.

Would we still use the ne explétif if the first part of the sentence was negative?

No. The ne explétif in comparisons is only triggered when the main clause is affirmative. If the sentence were negative (meaning the project isn't less costly), you wouldn't use it: Ce projet n'est pas moins coûteux qu'il imaginait.

Why is imaginait in the imparfait tense rather than the passé composé?

The imparfait is used because his imagining was an ongoing state of mind or an assumption he held over time before realizing the actual cost. The present reality (est) is being contrasted with what he was imagining (imaginait) during the planning phase.

Could I just say moins cher instead of moins coûteux?

Absolutely. Moins cher (less expensive) is very common and perfectly correct. Coûteux (costly) just adds a slightly more formal or professional tone, which is very natural when discussing a projet.