>that this Totality doesn't seem to be something over and above each of its parts, the totality is just a collection of each of those contingent things.


Yes, you are not missing anything. A totality is not identical to its individual parts, though. A totality is identical to the *sum* of its parts. But I do not think that this is at all relevant to the argument. The only thing that matters is that this totality exists and thus is a being.


>So if there is an infinite number of them then it seems it could have a mere internal explanation.

Making it a necessary being and so we can skip to the conclusion. (although Once we start talking about the traits of the necessary being, we can see that the BCF does not have them and so is not necessary making the BCF contingent).

Like John said, we can use different terms if it makes it easier for you to understand the argument.  I only use contingent/necessary out of respect for Ibn Sina. The same reason we still use "motion" when talking about the First Way instead of change.
 

Check the update, their objections are to an older argument.

Jimbo28 wrote:

There's a lot here, but I just want to look at one thing you said. 

Noble_monkey wrote:

Every property the necessary object has must be a property it necessarily has

This is problematic. If every property the necessary being has is necessary, then its property of having chosen to create the universe is necessary. One potential problem that comes up here is the freedom of the necessary being. If you believe that alternative possibilities are required for freedom, then it follows that the necessary being is not free.

But more importantly, if the choice to create the universe is necessary, then it follows that the universe itself is necessary. If there is no possible world in which A does not exist, and no possible world in which A does not cause B to exist, then it follows that there is no possible world in which B fails to exist, which is another way of saying that B exists necessarily. 

This of course contradicts the starting premise that there are contingent things. 

Ibn Sina does not have the same thing in mind as you have by property. Perhaps, "attribute" is a better word.

>It is also doesn't appear to me that an essentially ordered chain of causes, that regresses infintely, is impossible.

Has nothing to do with Craig's argument.

But yes, the argument is defensible.

It can't be the laws of physics or anything not-God because Aquinas proves that the prime mover has all the divine attributes including intellect, will and power in Questions 3 through 25 here (https://dhspriory.org/thomas/summa/FP.html#TOC02). 

I don't think that we have to go through all the alternatives one by one since this is not an abductive argument rather we can just directly prove that it is God with all the attributes.