Depends on the food. For vegetable soup I just toss the cubes in with everything else but for cream soups I make the cubes into stock separately. I've never tried adding them to non-soup dishes directly because they're very concentrated and I'm not certain their seasoning would distribute properly, depending on the dish.
Cubes are a substitution, and while a super common one, are not quite the same thing. That said, yes, you do not need to turn them into "stock" by pre-dissolving first.
You may try and if your stock cubes will not produce lumpy sauce or whatever you're cooking, you don't need to mix them prior. Stuff usually disolves better in cold water.
That is right, you can dissolve faster in warm water. However, some ingredients tend to form lumps in warm water - the main thing to watch out for is starch, commonly used to thicken.