I bought a new unopened package of mascarpone cheese yesterday and forgot to put it in the refrigerator overnight. Is it still good to use?
Mascarpone cheese is NOT made with a culture. It therefore needs refrigeration, sealed or unsealed. You really should throw it out.
Any dairy product not specifically labeled as safe for room temperature storage (processed cheese, UHT milk) must be kept refrigerated. If it spends more than 4 hours in the "danger zone" (40-140F), it should be discarded.
That depends on how it was packaged; check the label. If it does not say something like "refrigerate after opening" or give a shelf life, assume that it must be refrigerated at all times and discard.
Note that this advise is very conservative, and you will have to evaluate your own tolerance for risk.