Is my cassette or chain worn out? I bought this road bike as my first road bike in 2011. I have not changed the chain or any parts on it since then and I bike on it almost daily. It's been running great, but sometimes I have trouble changing gears and I feel like the issues are getting more frequent. I had a major accident on this bike in 2012 learning how to use the clipless pedals but the bike landed on the opposite side of the cassette. 

Are the scratches in the picture below "normal" for a bike this old? Do I have to replace any parts? Is it safe to ride as-is? 

Here are some pictures:
Use a chain wear gauge to see if the chain needs replacement (e.g. Park Tool CC-3.2).Generally, these err on the side of replacing a bit early, but if you want to be pedantic about it, you can use the Sheldon Brown link below to measure with a ruler. 

As for the sprockets or chainrings, I'll defer to this page by Sheldon Brown. The upshot is that worn teeth look like ramps and a non-stretched wont sit properly in the sprockets as shown in the image below (from Sheldon Brown)