> The set of people to whom I speak of does not contain major theist philosophers.

Intellectually sophisticated theists usually have some awareness of the arguments of (at least some) major theist philosophers. Maybe you never speak to intellectually serious theists?

> The essence of arguments you wrote boil down to assuming that god has no property which falls into the category of “must have cause outside itself”. Such a belief is without a firm basis in my opinion

I think your criticisms are targeting the wrong point. That God "has no property which falls in the category of 'must have cause outside itself'" is true by definition, given the classical theist definition of God (and even by some non-classical definitions). If something has a cause outside itself, by definition it cannot be God; if it (somehow) turned out everything has a cause outside itself, it would logically follow that God does not exist.

I think it makes much more sense to target the premise "everything having P must have an external cause lacking P". For the Kalam argument (for example), that would be "everything having a beginning in time must have a cause lacking a beginning in time". The burden is on the advocates of the Kalam argument to convince people that premise is true, and personally I don't think they've succeeded, and I doubt you would think that either.

> At any rate, any believer in an eternal god must be comfortable with the notion that things can exist without cause/beginning/whatever term one wishes to use.

Yes, but they conditionalise that comfort. Many theists would say they are comfortable with changeless entities existing without cause, but not changing entities; or necessary entities but not contingent entities; or timeless entities but not temporal entities. As a result that comfort of theirs extends to God but not the universe. Is their conditionalisation of that comfort legitimate? How do we even begin to answer that question?

Myself, I believe in God, but I'm unconvinced that any cosmological arguments actually work in demonstrating God's existence. So I think you are right to reject them. But I think some of the specific reasons you give for rejecting them are misplaced, overly simple.