Here are some ideas about it

1. The definition of free will, frankly speaking this is a highly empirical term as well, people are required to assess the factors that influence people’s judges, the main idea is how individually people could make decisions out of the environment (obviously the environment did have a impact on people’s decisions, a simple case, the temperature rises and people feel hot and maybe come up with an idea of taking off the clothes.)

2. the demonstration of the determinism, sadly, the determinism itself could not be proved in any rigorous way, the support of it is highly empirical, comes with science history. If u look into the history of physics, it is built on empiricism, and be included into laws, and apply them under certain uncertainty, the necessary of uncertainty is related to the way we acknowledge the world, it could be better understood with the help of materialism, as the so called objective truth and absolute truth. And we might come up with the quantum mechanics which seems to lose th characteristic of determinism, but we need to remember the world before newton’s three laws, the movement of rather big subjects still show a great uncertainty. The tricky point is we can’t deny the existence of determinism simply because of quantum mechanics, it could be a intermediate process as well. But according the logic relationship of past science history, it works. In short, experience, laws(approximate), and predictions(approximate), obviously, so far it’s impossible to say whether it’s right or wrong, but the main idea behind it, seems indicate the determinism works.

3. the problems we might encounter if free will doesn’t exist.

Of course, the first comes with the idea, if my behaviors are decided upon the environment, why I should hold responsibility for it.

This question could be sovleld by mutual benefit theory, the so called laws and rules are the tools we used to coordinate the beneficial relationship between individuals. And the main idea shows that even if free will doesn’t exist, people still need to hold responsibility. It is quite similar to the idea of Darwin: the nature selection.

4. If free will doesn’t exist. Does it mean u could have more freedom or less?

Well, the tricky point about this is though logically speaking, if determinism works, then everything is determined already, but the reality is we still couldn’t tell what would happen for sure, the reason is obvious: there are too many arguments. But If we have already know some empirical laws, especially psychological ones, then we could apply it to the environment to make the the following stuff become easier, the case is just like the relationship of temperature and feeling, but if it is applied in a more complex situation, we could make things easier by change some environmental factors around individuals. In this way, u actually have more freedom.