No, supply vents do not need filters. Having filters is an option that you can choose to help with filtering the supply vent. However, depending on the home, you may not need to use them. Even some supply vents use technology to help filter the vents, so you do not need a filter.
Kitchen hoods should either be cleaned monthly or quarterly to stay within guidelines. However, they need to be inspected weekly to ensure there is not too much grease buildup. If there happens to be a considerable amount of grease and other dirt, the hood can be cleaned during a weekly or monthly deep clean.
For inspections, ensure you are following the correct requirements and guidelines. Below are the requirements for inspections to happen in different kitchens: