Scientists are coming to the point of understanding the complexity of the universe that with independent fundamental physical constants at their exact values allows it to exist as it does with us in it to observe it, if the universe developed as their theories have described it, such that they on that basis say this is one of many universes in a "multiverse" and it is the single one that worked out, with no other basis for that conclusion. Science has not disproved God, but rather, because science as it is practiced cannot take God into account in any theory or observation, and so anything else for an explanation for things like this are grasped.
1. Yes, science cannot disprove God. But "science" is neutral on whether God exists. Remember, over half of living scientists believe in God. So there isn't an universal motive for disproving God.
2. That science "cannot take God into account" is a limitation of how we do experiments. If you are not sure how this happens, then ask me and I'll go into detail. But this "cannot take God into account" simply means that science is
neutral in regard to God's existence.
3. Yes, many of the fundamental physical constants
appear to be independent and arbitrary. They need to have the values they do in order for us to be here. However, those values are not mandatory; if they were different we simply would not be here to wonder about it.
One of the attractions of String Theory is that many of those apparently arbitrary constants are dictated by the underlying reality of strings and 'branes.
Now, things that are very improbable beg an explanation. The job of scientists is to consider
all explanations we can think of. One possible explanation for the improbability of the constants in our universe is that there are an infinite number of universes (multiverse) in which the constants are due to chance. If that were the case, then the odds that
one of those universes would have the constants we observe is virtual certainty. We, of course, happen to be in that one.
The next step after coming up with the hypothesis to explain the physical constants, whether God created and chose them or String Theory or multiverse, is to
test the hypothesis in an attempt to eliminate it. So far String Theory is failing testing and it is not possible to test God created or multiverse. So science is agnostic.
But you are wrong that "things like this [multiverse] are grasped". They may be "grasped" by some atheists (altho most atheists I have encountered tend to go for Aristotle's "the universe has always existed"), but
science is not doing that. Instead, science is doing what it is supposed to do: advance hypotheses.