Do people choose their personalities? If the answer is "no", then how does it logically follow that people are...

Replace "their personalities" with "whom they are," and now answer the question. :P

I did, really, by pointing to character. With a few exceptions (mental illness, addictions and some extreme situations) everything people need to be relatively successful is about patterns of attitudes and choices over time. People are responsible for choices. Some repeated choices reduce the ability to make good choices later - but we're responsible for that.

Explain how they're responsible for their choices.

Because they are choices. If we can't choose, we're not responsible. If we can make a choice - we are responsible. If an athlete decides to never train, he's responsible for being too unfit to finish a game. If we never learn self discipline, we're responsible for being unable to hold it together when we need to. Why? Choices.

Do we have control over what has happened in the past? Do we have the ability to change the past?

No. We have control over our next decision. There's always a best next decision. Same deal - an athlete realises he's unfit, he can start to do something to change it. I've had lots to do with addicts, people with mental illness and people who have screwed their lives up. I'm not theorising.

Are events that happen in the present dependent on events that have occurred in the past?

In logic, you're possibly heading for an equivocation (a logical fallacy) with the word 'dependent'. If you make a choice or series of choices and reap the consequences - yes your present is 'dependent' on the past that you can't change - whether it was 2 years ago or 2 seconds ago. Still responsible, go to jail, do not collect $200. But you still have a next choice. We're not trapped by the past - we just pay for it. We can build positively from wherever we are.

Is there not a chain of events connecting the past to the present? Do events in the past not have an effect on the universe? Do you disagree with me when I say that the big bang has started a continuing chain of events that has led up to this moment? How do we have the ability to make free choices when we have no influence over the first link of that chain?

It's a logical error to say that because we can't change the past we have no control over the present. You chose to ask this question. Nothing made you do that.

An incalculable number of events had to take place in order for me to ask the question; my conception, for instance. If I hadn't been conceived, I wouldn't have ever been here to have asked the question. In order for me to have not been conceived, the events that led up to my conception would need to be changed. For instance, maybe, the phone rings right before my parents go at it and it's a salesman, and they end up not doing the deed. But in order for the phone to have rung, the events leading up to the phone ringing would need to be changed. For example, the number that the salesmen called would've had to have been put on his list. But you would have to change something in the past to make way for the number getting put on his list. And so it would go until you were all the way back at the beginning of the universe. What we do is fixed from the beginning.

Your reasoning is just logically flawed. And you don't believe it. If someone in the street robbed you and shot you in the spine so you could never walk again, and then they got caught... would you stand up in court and say, 'they can't help it. It was predestined from the Big Bang?' No, you would expect the court to find them responsible for their actions. If what you say is true that it's all fixed, the logic of courtrooms is nonsense. But deep down, you'd want that justice because deep down you know we're all responsible.

It could be logically flawed, I'll admit that. I'm not going to say that I'm absolutely certain; there is always room for doubt. And I wouldn't think that they were responsible, but, of course, I think that they should still be isolated to protect society. The beautiful thing about determinism is that you can focus on more important things than senseless retribution. And you said my logic is flawed? How could I get shot in the spine and be unable to walk, and then stand up in court?! ;)

Justice isn't senseless retribution. It serves several different functions that can build better societies, including the possibility of reform - a major component of which is helping people take responsibility for their choices. An internal locus of control is also a key characteristic in those who (according to statistics) consider themselves to be fundamentally happy.

I think belief in determinism (the incompatibilist kind) could build better societies; it can prevent people from getting angry with each other and can effectively ameliorate tensions which are a result of hate-filled intolerance of other people's views; we would be able to focus on the isolation of and the protection of society from criminals rather than self-serving, vengeful sadism... But the efficacy of our beliefs doesn't say much as to whether or not they're based on truth; there are many things which we could believe in that would undoubtedly make us happier, but whether or not a belief brings us happiness is irrelevant as to whether it's based on truth or not... If I were to put my argument in the form of a syllogism, I believe it would look similar to this...
Premise 1: The initial conditions of the universe determine subsequent conditions of the universe.
Premise 2: We have no control over the initial conditions of the universe.
Conclusion: Therefore, we have no control over the subsequent conditions of the universe. In other words, we don't have the ability to make free choices.
I don't understand how my logic is flawed. I'm also not exactly well-studied in this, so if my logic is flawed, that might explain it.

I'm somewhere in between. We have have some ability to make choices within the limited hand dealt to us. I don't believe in the extreme that blames the poor for not succeeding - not the other extreme that says we have no control at all. The flaws in the syllogism are 'universe' and 'determine'. 'Universe' is not one entity, but many and might involve many entities making choices that lead to outcomes. Those outcomes may affect the next generation but do not necessarily remove their ability to also make choices. The word 'determine' can have two meanings - i. Have results; ii. Control. The influence of the past has results in the present. It doesn't follow that because we can't control the past, we have some control of the present.

I apologize for responding so late... What if I changed the syllogism into this? Given the initial conditions of the universe, there could only be one possible series of events across time. Because there is only one possible series of events, any event in the future is inevitable or, in other words, unavoidable. This would mean that something I am going to do, say, several years from now was already going to happen billions of years ago. Therefore, I don't have free will. "The influence of the past has results in the present." Results of which include the choices we make, no? I agree with that last sentence of yours, but I don't think it's what you meant to say.

Your syllogism is logical, but based on an assumption.
1. Given the initial conditions of the universe, there could only be one possible series of events across time.
2. Given the conditions of the universe, there can be many possible series of events across time.
Which is true? Your answer assumes the first one without any evidence.

Evidence for free will: When I make an achievable choice, I consider options and make a decision before I act. What I choose in advance happens in the future. People universally acknowledge this experience. Therefore universal experience is that we have free will.