I have found the e-books of Cassius Amicus the most valuable resources for Epicurean philosophy in the Internet. So I am happy to be allowed to join this forum.
Here are my thoughts about the aforementioned topics:
Existence of supernatural gods
Nothing, which is relevant, is beyond empirical investigation. Because if something has an effect on us, then it can be empirically investigated. And if it has no effect on us, then it is irrelevant. Therefore the gods cannot be supernatural. They are either natural, i.e. subject to empirical investigation, or irrelevant.
Pre-birth or post-death existence of souls
The state after death is the same as before birth. And since we cannot remember anything before birth, it is probably not important.
Existence of "ideals" elsewhere in the universe
Ideals are concepts of our mind. They have no independent existence apart from their usefulness for our thinking.
Whether knowledge is possible
We can know everything that we need to know. If something affects us, then we have plenty of information at our disposal to form our theories about it. If something affects us only a little, then we have little information to form a theory, but it is also of little concern to us. If something does not affect us at all, then we have no information about it to form any theory, but it is also of no concern to us.
Absolute truth is irrelevant. Knowledge is only relevant as far as it is useful for our life.
Role of reason, the senses, anticipations, and feelings in knowledge
Knowledge is based on observations (senses) and logical deductions from them (reason).
Anticipations are the tools that our mind uses for logical reasoning.
And feelings (positive or negative qualia) tell us what to seek and what to avoid, which is the purpose of all logical reasoning.
I generally agree with Epicurus with the exception of Epicurus' assumption that there is no pleasure beyond the avoidance of pain. There is positive pleasure. Therefore withdrawal from society and a passive life to avoid any unpleasant adversities is not the ultimate goal of happiness.
This is the summary of my views of Epicurean philosophy.