A compound is a combination of two or more elements.
A mixture is the same as a solution, containing the solute dissolved in the solvent. A mixture could also be defined as a colloid or a suspension.
There's no general method. There are processes that will separate mixtures, but not all work for all mixtures, and it's possible some would cause a chemical reaction (for example, trying to dissolve a mixture of sodium and potassium in water). You need to have some idea what the substance might be (just visual appearance should narrow it down a lot)