1
Diffusion (which includes facilitated diffusion) and osmosis are passive. This means that they do not require any energy input; they go ahead spontaneously.
Diffusion happens in a cup of tea, particularly just after you add some sugar. The dissolved sugar will gradually spread through the liquid. (But it's quicker to invest in a teaspoon!)
The active in active transport refers to the need for a supply of energy. In a cell this energy often comes from the hydrolysis of ATP.
2
Osmosis involves the movement of a solvent, which in cells is always water. Many substances can diffuse, but in osmosis it is only water molecules that move.
3
Osmosis requires a membrane that is permeable to water but not to solutes. Such a membrane is known as a semi-permeable membrane (or selectively-permeable membrane, or differentially-permeable membrane).
4
Diffusion can occur anywhere that atoms, ions, or molecules are free to move. Facilitated diffusion simply means diffusion across a membrane through special places in the membrane.
(This is like people going in and out of a room. In theory we could take a sledgehammer to the wall and enter anywhere, but our entry and departure is facilitated by doors. Many substances cannot cross a phospholipid bilayer, and must find special crossing points.)
Substances cross cell membranes by facilitated diffusion through special proteins, called channel proteins and carrier proteins.
5
Active transport is always through carrier proteins. This kind of protein is highly selective (for example, one type of carrier protein moves sodium ions one way and potassium ions the other way across the membrane) and changes shape during the process, reverting to its former shape when the substance has passed through.