That would depend where they're growing. In parkland they're colourful wildflowers; in my garden (although it's a slur against them to say so) they're definitely weeds.
As Tom points out a weed is any plant that is growing in a place it is not supposed to be. If I have a tomato plant growing in with my lettuce, it is a weed. Dandelions at one point in time were a food crop, they were imported from Europe, and then went wild.
No, I don't think so....people eat them as in dandelion greens, also make dandelion wine.....my grandmother however, would disagree with me as she always disliked dandelions in her yard!
When they grow out of control in my yard? Yes, they are weeds. I did just read an article that their roots have some great cancer fighting properties to the though. So maybe I need to cultivate them instead.
Yeah. And they're really hard to remove too.