Also, there are some great tips on level design and stuff on youtube (just don't waste too much time here...) from Extra Credits (Extra Credits: Game Design)
Yes.
and an ode to Mega Man X level design from Sequelitis (adult language) you can get some insight into how to think like a game designer.
And yes. This video is the one who help me turning on my game design spirit. Meaning no adding features on a game because this feature is cool. But because it has a purpose, it fulfill a precise role in the game.
Also, this book is in my opinion a must read : http://www.amazon.fr/The-Art-Game-Design-lenses/dp/0123694965
Creating board games with paper is also a good exercice. Don't underestimate the power of the pen :)