Yes. They have the choice to follow that political view and/or doctrine or not. Even if it is difficult to follow or not, there is walways a choice.

They had the free will to subject themselves to the doctrine in the 1st place. They have, in effect, sacrificed their free will to the doctrine, so after that point they do not have free will. I suppose the case can be made that a person born into a particular belief system who knows no other options could be said never to have had free will. However, if even one person has broken free of that indoctrination, that means the possibility, and therefore free will, still exists. People DO relinquish their free will to governments and religions on a regular basis.

Yes.Because they choose to let their thoughts and actions be determined by their beliefs.That is a choice,(free will).

No. In a situation that ones thoughts and actions are determined by someone else, he has no free will. But, in my opinion, our will can not be determined. We have always a free will. Man has always the power on his/her own idea. We can be guided or influenced by others yet we have always the chance to change our mind. If not, than why persons in the same situation are acting differently? People in the same church, under the same influences (religious) do not act at the same manner.

I think you've answered your own question.

No one can be said to have their "thoughts and actions 'determined (not merely guided)'...by someone else" unless they are the victim of a black ops program similar to the mind manipulation in the Denzel Washington movie. (I can already hear the rumble; I'll tell you in advance; google and check for yourself. Various governments have been playing around with this concept for decades.) Each person is a free moral agent. I don't even know if inteligence quotients have anything to do with a persons susceptibility. Hypnosis works on a broad spectrum, but experts say one cannot be made to do what they are not inclined to do anyway. I don't know about that; I've never met a soul that would be 'inclined' to eat an onion like an apple! I can say of a certainty that the area of thought control has advanced FAR beyond what is portrayed on any screen. (Even remote manipulation is proven.) Recent evidence suggests mob and crowd control tactics have been used. (Heat sensation, uncomfortable and painful headaches, even voices in one's head are, have all been utilized.) 'Voices' heard audibly within ones own head is very disconcerting, to say the least. Medical and scientific journals reported on this phenomena some time back. Barring this type of interference, an individual is still responsible for his/her own choices and decisions. Even those who blow themselves to smitherines are making a choice and doing so of their own volition. They no doubt remain strongly coerced, even brainwashed to some certain degree. But they still operate within their own free will.

It's not quite right to say our thoughts can be determined by external forces. And it's not quite right to say that WE determine them either. There's a simple experiment to demonstrate this point: sit in a chair, alone in a quiet room, for 5 minutes, and don't think anything at all. Just stop having thoughts altogether. Go ahead: you have to actually DO the experiment. "Thinking about it" doesn't count. I'll wait. ...(5 minutes passes... :-) Ok, so now you know the truth: human beings cannot stop their own thought processes. Why? Because that isn't YOU thinking. If it was YOU thinking, then YOU could stop thinking, right? But you can't stop thinking, therefore it isn't you doing the thinking in the first place. End of story. So now what? Well if you keep following that trail, it leads to an interesting place: thought is prior to you, not the other way around. Normally we think "oh I exist, and then I have thoughts". But that's backwards. The truth is, "thoughts exist, and they produce ME". You are a product of thought. There's a more advanced experiment which demonstrates this point, and requires quite a bit of time and effort -- if you practice awareness long enough, the mind quiets down and thoughts settle down as well, to a very slow trickle. When that happens the sense of being a "self" starts to disappear. I can't demo that in 5 minutes, sorry. So the whole question "do I have free will" is in a certain sense bogus, because the "I" is a product of thoughts which arise unbidden, as do all of our concepts about free will and determinism -- they come from that which we cannot speak about, because the moment we form a concept about where they come from, that's just another spontaneous thought. Having said all that, when this constructed sense of self becomes "transparent" -- i.e. when we see it's true nature, the experience that is left over is one of freedom and creativity. THAT is real "free will", and the clarity about that in one's own experience resolves the question with finality.