People who are arsonist and terrorist usually undergo a psychological change which actually influences their consciousness and conscience as a human being, if you look very well you will discover that people who recruits this kind of people always take advantage of those that are weak willed or those that have suffered so much in life so they will take advantage of this happening to actually influence their moral belief and plant a different kind of mindset contrary to the original mindset before they become terrorist.
So one of the reason why they are heartless when carrying out missions like these bombing and setting places and buildings on fire it's because they are without moral empathy, sympathy and humanity towards the human race, and this is because all these have been totally scrubbed away by a stronger psychological effect because they were weak and easily manipulated.
Another thing that motivates them may be their hatred for their state people have so many reasons to hate their state for example sometimes it could be that they took away their jobs and their property and made them homeless or jobless.
These kind of people are always targeted by terrorist organisations because they do not have much to live for and as a result of this they're easily preyed upon and when they are going on missions like bombing places the people who usually recruit them actually reminds them that whatever they are doing is to get back to the people who have destroyed their lives and they are not actually reminded of the fact that they are going to end human lives
Well everything you've stated has different reasons for why people do such things but I think it all boils down to three things;
1. Misguided Beliefs: This is especially true in the case of terrorists, they usually have beliefs that may or may not be backed religiously. Its these beliefs that make them feel it's ok to take the lives of innocent human beings because to them they're doing the right thing and in most cases they feel their deeds have been sanctioned by God himself. If you ask me, it's the religious based misguided beliefs that are the most dangerous because they truly believe that what they're doing is right.
2. Insanity: The truth is that some people are just crazy, they're deluded and have mental illnesses that make them do certain things, certain evil things. They don't think like the rest of us do and as such killing innocent people either isn't that big a deal to them or in some cases makes them happy. You'll probably find alot of suicide arsonists falling into this category because they simply love to see things burn and it doesn't matter to them if human beings burn as well.
3. Evil people: There's no way to put it, some people are just evil, they think and behave like the rest of us but they seem to gain joy in watching other people suffer and die. It's not a matter of whether they're mentally ill, nope they're perfectly ok but for some reason they get their kicks from watching people die.
I hope this helps.
False beliefs...lack of empathy...cruelty and an enormous degree of human stupidity. Such people do not deserve to be called human.