Yes, you can. Caster sugar is merely smaller granules of granulated sugar.
If the recipe calls for caster sugar for appearance's sake, crush granulated sugar under a rolling pin or glass bottle.
The total weight of sugar is what's crucial, so no, you need not adjust weights.
Poodicat's spot on... for any dense mixes it shouldn't make any difference, or for any recipes where the sugar will be dissolved. BUT if the recipe calls for the sugar to be used as a binding agent, such as in a beaten butter & sugar base for biscuits or cakes, or especially in a beaten egg & sugar mix for creme brulee or ice-cream, then it's important to use the finer caster sugar or the resulting dish may be grainy or even split.