Can one tear Saran Wrap on shabbos, to cover food to keep it fresh, for example on Friday night to keep food covered and thus fresh for shabbos lunch? Can one do the same on shabbos day to keep the food fresh so that the food doesn’t go bad even when the food will be eaten after shabbos?

ב"ה Shalom One is not allowed to tear Saran wrap (or other clinging plastic wraps) on Shabbat and even without the cutter. Using the cutter to cut the desired size would be even more severe since it would be a Torah prohibition. However, if one cuts a few pieces of wrap before Shabbat and has them cling to a clean dish, there is no problem using them to seal a dish with food. Also, today, there are companies which produce food covers already prepared in different sizes with a rubber band for sealing, similar to a shower cap. (I have not seen this in Israel, but today almost everything is available online). Aluminum foil is also available in precut pieces not to mention that there are so many available reusable or throwaway plastic containers to seal food so there are many solution for keeping food properly stored on Shabbat. All the best