Do you draw everything for your games by yourself? Have a designer?
I'm a designer, so yes, I design everything myself because that's what I'm good at. What I normally lack is a programmer, and because Construct is so simple, I don't really have a problem with that with the projects I do now.
Have a whole team?
I normally work alone.
Download images from free stock sites?
Never.. there aren't much free graphics out there which can let you make a full game without at least making a little bit yourself, or getting pieces from elsewhere and mismatched graphics is bad.
If you want though I recommend
What about music?
There are lots of sites out there which you can get free music and sound effects from
Flash Kit, Newgrounds, OpenGameArt are just some.
But always check the licensing, never use a piece with a license not legal for the game you're making. Don't use non-commercial licensed music for a commercial game and give credit when necessary.