Whence did you obtain the first two premises
The process is rather simple.
One has to try to put the argument into steps.
Then it will be clear that some steps do not really follow from anything before them.
And that’s when one has to fill them in by new steps, new conclusions, or new premises.
It is easy to notice that Russell’s argument was meant to take two possibilities of Law of Excluded Middle (“everything must have a cause” or “not everything must have a cause”) and to apply the rule called “disjunction elimination” in Natural deduction. That’s the step 4.
Now in “disjunction elimination” one has to derive the same conclusion from both possibilities. Russell does not give that conclusion explicitly, only “there cannot be any validity in that argument” in one branch, so I replace it with “existence of [God/empty set] is doubtful”, which is equivalent and avoids ambiguous “that argument”.
Now he does not have any explicit premises that connect the propositions he starts with with “existence of [God/empty set] is doubtful”. But it is clear that conclusion is going to be reached using “Implication elimination”. So, to connect them we need premises with implication. The ones like “If [God/an empty set] must have [a cause/an element], existence of [God/empty set] is doubtful.” and “If [world/set of natural numbers] can be a [thing/set] without [a cause/an element], existence of [God/empty set] is doubtful.”.
and why is premise 3 unjustified and unreasonable?
It is unjustified, because it is not given any justification.
Russell just proclaims: “If there can be anything without a cause, it may just as well be the world as God”, he does not argue for this claim.
For first two premises one could make a justification using “if false, then anything” (or “Contradiction elimination” in Natural deduction).
For this one no justification can be seen.
And, of course, it is easy to see that there will be no good justification, because we can’t justfy false propositions.
And in case of “empty set” we can easily see that premise 3 is a false proposition, because if we add it to true premises 1 and 2, it is possible to construct this same proof of absurd (and thus false) conclusion “Existence of [empty set] is doubtful.”.
So, we can see that premise 3 is not going to be true just because of its form. And thus it needs a justification. The one which was not given.
We can also see that premise 3 is unreasonable by directly looking at it: “If not every [set] must have [an element], it might be that a [set of natural numbers] is without [an element].”. Well, why “[set of natural numbers]”? We already know various things about it. And one of them is that it has infinitely many elements. So, it can’t possibly have no elements.
And likewise, we already know various things about the world. For example, that it does change, come into existence. And, since we know that each change and coming into existence needs a cause, thus we already know that it needs a cause. Merely claiming “But what if it is!” is not a sufficient justification.