If they want to kill innocent people because of their beliefs, they are dangerous and should be shot/arrested for intelligence gathering. The public needs to know that the government is taking direct action to stop terrorists. Terrorists should not have the public's tax money wasted giving them a trial when they want to kill innocent people.
When they are engaged in a terrorist act or have been proven to have masterminded an act of terror a terrorist should be shot dead on sight. Unfortunately this is what many terrorist would prefer as it would give them what they feel is a "hero's" death. A long trial and wasted resources is also a win for them so it would be better just to shoot them and move on, no memorial, no appeals.
No, supposed terrorists should not be shot dead on sight, unless there is an immediate danger and lethal force is the only force that will stop the danger. In any other case, a person is only a suspected terrorist and should be given the due process that is the right of every person.