When I've looked into some of the claims you mention I've found the argument for the contradictions more convincing than the arguments against. I'm reasonably comfortable with my objectivity and if you want to present the strongest refutation of any single contradiction I will give it due attention.
Not all of them, I hope, you find more convincing than the arguments against! Take the one concerning Judas dying by hanging vs dying by falling and his guts bursting open. You see no reasonable way both could happen?
As to the First Cause- Cosmological Argument I generally consider matters of Origin to be way above my pay grade. I leave that to the many millions on the planet who are smarter than me. I am inclined to say that your affection for the "law of causation" is quaint, but worry that sounds patronising - not my intent.
If you can handle the convolutions of Darwinism, I should think the simple logic of the Cosmological Argument easy! The so-called refutations that I have studied are either, in the final analysis simply illogical (referring to those that present a supposed alternative to first cause, or a supposed first cause possessed of illogically non-first-cause-ish characteristics), or they are refutations of the formal philosophical statements, and at that, usually simply semantics. (Actually, some of those I tend to agree with, though I'm not always sure what is meant by what I am reading, as I'm not trained in Philosophy.)
I've not yet been shown an effective alternative method. I'd delight in having one. I've read many claims, but no one has come up with the goods.
During childhood, instinct works pretty well. Love works wonderfully well, some times. And then, there's habit, though, granted, that is often, if not usually, based on repeated empirical findings and their conclusions, but it is not entirely logical in form.
That may well be the case. Does that trouble you? If so, why?
No! It is one of my happiest logical claims!
Yes, that might be the case. It's worked out moderatly well for me. Hopefully for you too.
It seems that if it is true, I like how it was done! But both this and the other, (that only one thing ever happens), don't seem to change anything except to get people upset, perhaps.
Being married taught me that intelligence is not always, (in fact, maybe not usually), logical —not to mention that logic is not always intelligible. It also taught me that good sense had better have a good sense of humor, or one might go mad with logic.
When I argue I might appear to take myself seriously, because it seems to acquire and keep the upper hand more easily, but I think intelligence should know better than to take oneself too seriously.