Dennis:

A root cellar is what you need. A google search turned up lots of info.

As far as what part(s) to eat... Research each vegetable. Squash blossoms
yes, potato blossoms no.

Turnips, there are greens types and root types. Can you eat the other part
of a turnip? Sure. Will it be as good as the type for the use? Probably
not.

Storage also depends on where you live. Carrots can be stored under straw
bales in the ground. We freeze and can mostly.

Onions, I chop fine in the food processor and freeze thin enough to break
off pieces. Same with peppers.

Good Luck and happy Gardening!

John!