How to fix/avoid these problems in future pictures?

I'm new to DSLR, and am currently using the Nikon D3100.

I went to a bike convention, and noticed some pictures came out strange.

-there was a slight purple tint in areas of the picture where there wasn't IRL.
-strong lights behind an object make the picture come out weird.

Here are some examples:
http://www5.snapfish.com/snapfish/thumbnailshare/AlbumID=3225701025/a=4916850025_4916850025/otsc=SHR/otsi=SALBlink/COBRAND_NAME=snapfish/

How can I fix/avoid these problems in the future?
thank you.

Added (1). The lens thing - i bet that's it, i'm using the one that came with the camera.

any suggestions/tips where/what lenses to get are?

It's called "purple fringing" caused by chromatic aberration. You are probably using a low end lens. You can only avoid it by avoiding bright, high contrast things in your photos. Or fix it in editing http://www.google.com/...=firefox-a

To avoid this never shoot on front of a light or mirrors or something that reflex light
anyway is you do so get a polarized filter this filter controls high colors and will help a little to get a better shot, also if you have an external flash bounce the flash and you will see the difference
or if you do not use a flash, use a fast lens 2.8 or lower like the 50mm 1.8 is it inexpensive and works great, low shutter speed like 60 to 80 high iso like 800 and aperture really low
i went to the autoshow at night and many ppl gets frustating cus of my flash, so i use high iso low aperture and low shutter speed pictures turn out awesome