Basking is sitting or lying in warmth, enjoying it. You can also bask in something pleasant, as in "she was basking in the attention". Lizards like to bask in the sun because they are cold blooded and the sunshine warms them up.
A cask is a reasonably small container, usually used for storing alcoholic drinks. Casks are usually shaped like a small barrel, although the term is often applied to cheaper boxed wine too.
Damask is a pattern used on a variety of fabrics like silk and wallpaper. Damask patterns can come in a lot of different designs, but the most common is a damask rose pattern like the one in the picture.
A dust mask is something you wear over your mouth and nose so you don't breathe in particles of dust or smoke. People usually wear dust masks as protection when they are on a building or contruction site.
A flask is a type of bottle. There are different kinds of flasks. A conical shape glass flask is typically either used for chemistry. Squarer flatter flasks made from metal or glass and about the same size as your pocket are used for carrying a small amount of a strong alcoholic drink like whiskey.
A mask is something you put over your face. Some masks are used by doctors so they do not breathe on you in a hospital. But many masks are pretend faces that are fun to wear, and make you look like a monster or an alien or just a different person.