at this point, i suggest replacing your charger. You can show it to the apple store and hope you'll get a free replacement. stop using your damaged charger, you don't want to risk any fire or any injury.
regarding your computer, your rom was probably wiped that's why all the pw and date settings were reset as well. once getting the new charger, set the date and your pw and see if your computer will still reset everything after shutting down.
You can get a new third party 60W power adapter on eBay for under $20.
http://www.ebay.com/sch/i.html?_nkw=macbook+power+adapter&_sacat=0&_sop=12&_dmpt =Apple_Laptops&_odkw=macbook+power+adapter&_osacat=111422&_trksid=p3286.c0.m270. l1313
Or for $80 from Apple http://store.apple.com/us/product/MC461LL/A?