Humidity can be gotten around with packaging, damp sand or
straw or even an open bucket of water. One issue is that the storage temperatures are very very different, garlic want's 0C (32f) whereas potatoes want 7-10C (45-50) and sweet potatoes need over 12C(54F) or they take cold damage. Humidity requirements vary from 95% right down to 50%. A good list of optimal storage temperatures, damaging temperatures and humidity levels can be found
HERE
I'm not sure what you would call my cellar, it's the house cellar but I think it's closer to what people on here call a root cellar than whatever a Basement is. It's Brick, whitewashed uninsulated and has two small single glazed windows facing north with a always open vent. The temperature in high summer is around 13C and in winter about 1 or 2C when it was -18C outside the cellar was at 1C. (there is an insulated central heating pipe that runs through it stopping it freezing in cold weather) I use it to store potatoes(yes it's to cold but it's what I have), carrots, parsnips, onions and garlic. The potatoes are on the floor in hessian bags and keep fine, the carrots and parsnips have to be in wet sand or they dry out the onions and garlic hang from the ceiling. Winter squash and pumpkins are kept in the house in a cool room at around 15C the cellar is way to cold for them. The humidity in the cellar is close to that of outside so about 90-99% all winter.
If you were to keep the area at around 12C (54F) you could keep the onions and garlic for a few months, the squash and potatoes would keep nearly to their maximum and the sweet potatoes would also be happy. You would need to do some packaging on the items that like higher humidity.