A mere cursory glance at the European locks forums would reveal stickys on the subject of lever locks, complete with pictures
A back door lock should be a 3 lever at least, normally a 5 lever, and not a lousy 2 lever ( for internal doors only) as you indicate.
If it's a two lever then blowing on it should open it ! A three lever is fairly easy if you know what your doin, and I'd forget it if it's a five lever unless you have the right kit and really know what your at.
By the sounds of it, you have "opened" up the hole ? you may in the process have made it harder to open by compressing the case and preventing the levers from moving properly.
As for a drill point , you need a locksmith for that
