Yes
Yes it is like switching form Cabernet to Pinot Noir
yes
Burgundy is a region in France that produces both red and white. Commonly when someone says "Burgundy" they are referring to the red wine made with Pinot Noir grapes. That would be a good red-wine substitute if you can't find Burgundy at your store; try to pick up a California or Oregon pinot noir instead. They also make white wine in the Burgundy region; primarily it is made with Chardonnay grapes. Thus, if you have to find a substitute for white Burgundy, then get some Chardonnay. A good rule of thumb to remember when cooking with wine: If you wouldn't want to drink it, then don't cook with it. Buy something decent, not something cheap.
Burgundy wine can refer to red wine, made from Pinot Noir grapes, or white wine, made from Chardonnay grapes, though there are other varieties of burgundy, made from various varieties of both red and white grape.
piesporter wine, I think
Any red wine can be substituted for Burgundy when creating a sauce or making a casserole such a Coq au Vin. Cheap Roses are excellent for adding a fruity panache to such dishes and easy on the budget.
An aligoté is a variety of white grape and white wine from Burgundy.
Only if it is white or rose.
It is best to use a regular burgandy (not a cooking wine) in cooking. Cooking wines often contain salt and can change the flavor of the dish. I'd choose a moderately priced wine intended for drinking.
Red wines are red, Bordeaux wines can be red or white but they must come from the Bordeaux region of France
French Burgundy is pinot noir if it's red, chardonnay if it's white. The subsection of Burgundy called Beaujolais is made from the gamay grape. You will also, rarely, find the white grape called alicante bouchet.
A heavy white would work, like a white burgundy.