Can manual discounts and promotions be used together?

Yes. The rule is “manual wins, layers stay independent”:

• Manual item discount: that line no longer receives item-level promotions — your manual discount is treated as the final on-the-spot decision. The line's amount still counts toward spend thresholds, though.
• Manual cart discount: applied after all promotions have been calculated, so the two coexist. If you enter more than the remaining total, it's automatically capped with a notice.

Removing a manual discount restores the line's promotion eligibility on the next evaluation.