2005 Chevy Impala steering wheel vibration when braking aft

Shakes or Wobbles problem
2005 Chevy Impala 6 cyl Automatic 69000 miles

Hi. I would like to know why does my car & steering wheel shakes/vibrates after pressing on the brakes while doing 50mph? Also my igition is not on correctly. There is some extra space/ loose. The car digital panel shows the word security & I use a key padlock. Lately my car hasn't been able to start without a jump, so I read my manual guide & it states something about fuel is not transferring over or something. I wanted to know if thats true or could something be wrong with the alternator? Because now the the car doesnt acknowledge the key padlock anymore. I always make sure all lights are off before I leave my car too & I had the battery checked recently too.