#1. I won't necessarily argue with this point since I don't have any reference there, but do you have the data backing that up? Because if we're just talking the price per day of keeping a person incarcerated for life, that's probably relatively low until you add in the support costs as well. Death is, well, it's a one time cost and the electric chair probably isn't that expensive if you catch my drift.
I actually prefer the guillotine myself. Simple, effective and probably not that expensive.
#2. I can partially agree, but I think one of the reasons it doesn't have the deterrent value is because it takes so bloody long to get it done. The average time between someone sentenced to death and their execution is 22 years:
U.S. capital punishment - average time between sentencing and execution 2019 | Statista
And it shows an upward trend. Now, I'm okay with the appeals process of the judicial system, but you and I both know heinous crimes don't get dealt with swiftly in our country and cheap lawyer tricks have lengthened the process. As well as the debate over death versus life in prison. The deterrent of the death penalty was lost a long time ago because of the sheer time involved in getting someone from the courtroom to the death chamber.
#3. I can agree with this to a limited extent even as little as 20-30 years ago. However, with modern technology and investigative methods, this should be (should being operative) a thing of the past. I'm not sure the case for exoneration really applies as much any more with crimes committed today.
Now, I will agree the older cases you hear about from time to time that may have been run slipshod or had shaky supporting evidence are causes for concern, but I'm of the mind that cases where clear and direct evidence of a person being guilty should be fast tracked as the deterrent as we discussed earlier. Honestly, the quicker murders and other felons of heinous crimes can be made an example of the better in my opinion.