When baking, when can you replace butter by oil ?

Butter is really all about flavor, and oil and butter are completely interchangeable fats, meaning if a recipe calls for a 1/2 cup butter, can absolutely replace it with a 1/2 cup oil, but the flavor will change, not how the cake will turn out. You can also use vegetable or animal shortening (lard), if you need to in a pinch. 

Not as a direct substitute, by weight or by volume, and mixing methods are different for butter and oil. There are plenty of cake recipes that are intended to be made with oil. Google to find one.

You can use just about any kind of cooking oil as a substitute for butter. It really depends on what kinds of flavor you want. I personally like the flavor from olive oil. But I know some people who do not. You can even use something like lard (animal fat).  Again, it's up to you what kinds of flavor you want the dish to have.

The use of butter in baked dishes is for Flavor, and while you Can use margarine, the flavor lacks. IF you want a sub standard product, use margarine. 

Margerine is a useful substitute, or you can look for bakiing fat like a brand called Cookeen or Stork SB- available in Britain. Don't know if you get that in Asia. I used vegetable oil to make pastry last night and it wasn't great - but I am rubbish at pastry. Sad cat face emoji.

You can do anything you wish.

but....

Butter tastes Better.  If you enjoy your food, you must use butter.

Per serving, butter is NOT too expensive.  30 years ago I checked the cost of butter vs. vegetable crap -- it was two cents per large chocolate chip cookie.  Is YOUR child worth two cents?

No it will taste wrong. Try vegetable oil spread. It's cheaper than butter and tastes like butter 

It depends on the recipe.