To create web designs you don't need to know any of those things. These are things needed for developing websites not designing them... assuming that the OP isn't confusing the two.
I have dealt with a lot of designers and most have almost zero knowledge of HTML and CSS. They give me a template ... sometimes just a flat image, and I html'ify that.
It is nice to work with a designer that has some concept of HTML and CSS. However I won't accept HTML/CSS from designers anyway as the markup is never how I want it.
Mini, if you are talking just doing design.. get good at 1 design tool.. Illustrator is a great tool for creating web and print work IMO. The more you stick with 1 tool the more you will master that 1 tool. If you want to create templates from your designs you can check out Fireworks.
It would be a strange situation if you submitted artwork for a project and they asked you to make it in Quark instead of Illustrator.
IMO... The only reason to learn something different is if you want to work somewhere that uses something different or if you aren't happy with the tool you are using.