Air pushing under basement door and kitchen sink cabinets when furnace runs
You are supplying heated (or cooled, in season if it also does A/C) air to the basement, but not providing a return for it in the basement, so it's traveling to a return on the first floor by any means it can.
As you properly suspect, the cure for this is a return in the basement. Placing the return low in the basement will return colder air (good in heating season.) If you also air-condition you might want a way to switch to a high return vent in the summer (such as having one low, and one high and a damper to choose between them.)