1. They are talking about whether the death penalty should be abolished.
2. No. Sentence 1 means that the death penalty has not been abolished and the possibility of abolishing it is still hypothetical at this stage.
Sentence 2 suggests that 'the abolition of the death penalty' is an event which either has happened or might happen.
3. Both are correct. The 'on' can be omitted.
NB. Note my corrections to your sentences. You need to say 'the death penalty'. You cannot omit the article. This is a definite noun phrase referring to a particular type of penalty, so the definite article is needed. Also, don't forget to start each sentence with a capital letter.