I realise this may not be satisfactory, but many philosophers and scientists think that we cannot know the answers to your questions.
You start by saying that we know that beyond the universe there is nothing. But this may be one of the things that we cannot know. If there was something, something physical, before the universe then this would be the origin of the energy that gave rise to the Big Bang. One possible explanation, then, is that there are or have been many other universes (the multiverse theory). Of course, there is considerable difficulty (impossibility?) in collecting any empirical evidence for this theory, since such evidence would need to come from beyond the limits of spacetime itself.
But perhaps something - some universe or other - has always existed; there was never nothing. Many people find this claim more puzzling than the thought that once there was nothing, and then there was something. But why? The philosopher David Hume asked us to consider the limits of our knowledge about matters like this. It seems conceivable that something has always existed, and each thing has in turn caused the next. You may object that this just pushes the problem back. Your questions apply to any other universe as well. If this universe was caused by a previous (or another) universe, and so on, infinitely, that doesn't help. For instance, science tells us that time came into existence with the universe. Time itself ‘began’ with the beginning of the universe just under 14 billion years ago. That means that whatever caused the universe (if it has a cause) cannot exist ‘before’ the universe – there is no ‘before’ the universe! Instead, the cause of the universe must exist outside time. We think incorrectly then if we think that another universe, one that existed before this universe, caused this universe. If there is an infinite series of causes, this cannot be how it takes place. Hume might respond that we simply can’t know the answer here. So we should draw no conclusions. Bertrand Russell once said that the universe is ‘just there, and that’s all’.
Perhaps there was nothing and then something. What should puzzle us here? First, must everything have a cause? Hume argues that it is not self-contradictory to deny it. The same is true of ‘Something cannot come out of nothing’. That means that these claims are not certain. Our experience clearly supports these claims, but experience cannot establish that a claim holds universally. And we have no experience of such things as the beginnings of the universe. Second, the beginning of the universe is not an event like events that happen within the universe. For instance, it doesn’t take place in space or time, since both come into existence with the universe. We cannot apply principles we have developed for events within the universe, such as ‘everything has a cause’, to the universe as a whole.
When we turn to the question of God, there is the possibility of a distinct kind of reply. To think of God as self-causing is not usually to think that there was a moment in which God caused God's own existence. A better way of putting the thought, which some religious philosophers have done, is to claim that God's existence is necessary. God is the kind of being that must exist, that could not not exist. So God never came into existence. The philosopher Frederick Copplestone thought that your questions lead us to conclude that a God of this kind exists:
1. Things in the universe exist contingently (they may or may not exist, i.e. they can come into existence and go out of existence).
2. Something that exists contingently has (and needs) an explanation of why it exists; after all, its existence is not inevitable.
3. This explanation may be provided by the existence of some other contingent being. But then we must explain these other contingent beings.
4. To repeat this ad infinitum is no explanation of why anything exists at all.
5. Therefore, what explains why contingent beings exist at all can only be a non-contingent being.
6. A non-contingent being is one that exists necessarily, and doesn’t need some further explanation for why it exists.
7. This necessary being is God.
There are at least two problems with this argument. First, as Hume and Russell would argue, perhaps it is not true that every contingent thing requires an explanation for its existence. Second, it is unclear whether the concept of God as a being that must exist is coherent.
I haven’t answered your questions, but I hope I have given you a sense that they are widely shared!