Unfortunately a warranty does not cover an accidental damage inflicted by improper use. If you could prove that a battery lock didn't work than maybe. Otherwise the company won't pay.
Most likely not... if there are any visible scratches, cracks or dings it won't pass the "normal wear and tear" clause of the warranty. This situation sounds as if it would fall into the category of "accident" and would not be covered.
contact the computer manufacture about the issue, if you purchased a extended warranty then yes it should be covered, if you have a dell they offer accident coverage.
Normally batteries are not covered due to the fact that batteries degrade over time. Benq is a smaller company so most likely it is not going to cover your battery.
No warranties do not cover physical abuse. Most computer hardware will not. Only natural wear and tear. Also I'm surprised a battery still has a warranty of 1 year. The majority of the ones I have seen in the past and current only have a 90. Your options are to spend the money and get a new one.