Q: Is this normal for Macbook chargers?

Check to see if there is any debris in the charging port. Even small bits of things can make it wobbly.

I have no idea what you are trying to describe.

Apple Portables: Troubleshooting MagSafe adapters - Apple Support

The mag safe charger /connection are under the Apple 1 yr warranty or extended warranty if you are having an issue.

Genius reservation http://www.apple.com/retail/geniusbar/

on-line https://getsupport.apple.com/GetproductgroupList.action

check warranty https://selfsolve.apple.com/agreementWarrantyDynamic.do

I have no idea what you are trying to describe

It is a small magnetic adapter that allows an older plug to convert to a new style plug. Apple doesn't bother to mention things like this in support documents.

http://www.apple.com/shop/product/MD504LL/A/magsafe-to-magsafe-2-converter