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Cooking volumes are unusually inconsistent between countries, which is why recipes travel badly. A US cup is about 237 millilitres, a metric cup is 250, and an imperial cup used in older British recipes is about 284. A US tablespoon is roughly 15 millilitres while an Australian tablespoon is 20, a difference of a third that matters a great deal for baking powder or salt and very little for water.
The deeper issue is that volume is a poor way to measure solids at all. A cup of flour can vary by a fifth or more depending on whether it was scooped, spooned or sifted, and whether it settled in the bag — which is why the same recipe can produce quite different results for two people following it exactly. This is the reason professional and most European baking recipes specify weight. Where precision matters, particularly in baking, converting to grams and using a scale removes the ambiguity entirely; for soups, stews and anything forgiving, volume is perfectly adequate.
It depends on the origin of the recipe. A US cup is about 237 ml, a metric cup is 250 ml, and an older imperial cup is about 284 ml. Check where the recipe comes from before converting.
Most likely flour measured by volume. A cup of flour can vary by a fifth depending on how it was filled, and that variation shows up directly in the texture of baked goods. Weighing removes it.
No. A US tablespoon is about 15 ml and an Australian one is 20 ml. The difference is significant for concentrated ingredients such as raising agents, salt and strong flavourings.
For baking, yes wherever possible, since it is far more consistent. For cooking where proportions are forgiving, volume measures are perfectly adequate and usually quicker.