Thank you for writing a thoughtful post. I am going to respond to each through the lens of Stoicism.
Problem of freewill and determinism
In Stoicism we are taught and practice the Dichotomy of Control. The Dichotomy of Control teaches us that there are things that are under our control and things not under our control. Things that are under our control are our judgments of external impressions and our voluntary actions. Whereas, everything else is outside our control. Thus, Stoics would argue that freewill and determinism are not mutually exclusive but coexistent. Furthermore, Stoicism teaches that for those things that are under our control we need to act in a virtuous manner and for the things outside our control we need to be as indifferent as those things are to us. So I guess a Stoic would question why there is an argument to begin with.
The existence of God
Does the existence or non-existence of God in any way impact acting virtuously with what we have control over? No.
Does the existence or non-existence of God something that is in my control? No.
To a Stoic, at least in a modern sense, the existence/nonexistence of God is not really an issue. After all, if God exists and I act in a virtuous manner consistent with the nature that God created me then it is a petty God that condemns me to Hell for not worshiping him and him alone. If God doesn't exist then I still have a responsibility to fully realize the attributes that evolution has granted me.
Problem of evil
To a Stoic, no act is evil in and of itself. What makes an act evil is our judgment of the act. However, there must be a somewhat universal standard by which we can collectively classify certain acts. In my opinion, the best methodology to do this with is Classical Liberalism and/or a constant reminder of the following quote from the Meditation of Marcus Aurelius "We were born for cooperation...So to work in opposition to one another is against nature: and anger or rejection is opposition." The former values individual rights chief amongst which are life, liberty, property and the pursuit of happiness (to blend both Locke and Jefferson) whereas the latter so that anything that puts us in opposition with our brethren is unnatural and a vice.
Mind/Body issue
This is a non-issue to a Stoic because it is not under our control and in no way affects our ability to act virtuously.