Correct. In fact the cosmological argument was his main focus, but his main counter claim was that there was a third element to the cause- effect relationship. Something he was never able to prove. However, it was through the process of trying to counter these things are where his brilliance lies. His insight to causal relationships, the fact that you could reliably make predictions with a small subset of data, and things that did not fit the mold, had him postulating another element of causation, intervening between cause and effect, that must explain all of it.
It didn't. And again, he was a hard core empiricist. What he did not analyze was causal relationships that exist by definition, he dealt mainly with physical matter. His biggest problem was that effects followed their cause. So to him there was plenty of opportunity for another intervening factor.
Hume was a fearless philosopher, honest to a fault, and never had an issue painting himself into corners. But he made some very interesting observations with long lasting reach. It effects science the most, though.
He tried to disprove the thing you mentioned, he did not succeed at that, but he succeeded at other things in the process.
Monadology was considered strange by everybody. That everybody of space is occupied by something tiny, indivisible and permeates everything is a concept we are just warming up to now. Because, by all measures, he's right. There is always something, never nothing.
All metaphysics is the result of plato's forms. As much as I don't really like Plato, that gave birth to metaphysics. It was one of two things Plato was actually right on.
I am not attracted to a philosopher based on their religiousocity. Hume is one of my favorites of all time and he was an atheist. I am attracted to the ideas. Berkeley is also a particular favorite of mine, not because he was a theist, but because of his works on ontology.
I give Kant his respect, but never was a huge fan. His works on morality are important, but I always felt he liked to over complicate the issues. However, his ability to break things down, particular moral events are important.
Religion was never in danger. Aquinas did most of the heavy lifting and basically girded religious philosophy against the notion that science or anything else for that matter, could disprove God. He also was the one that realized the rule of nature, does not violate religion, in fact they are complimentary. Leibnez, expounded on those ideas, but Aquinas came up with them first.
It's Leibnez's scientific observations that interested me the most. I am less concerned about what he thought monads were than I am about the notions such an idea brought forth.