Hey Benjamin, I'm glad you enjoyed the article. As for your questions:

Quantum Fluctuations: the trick with explaining this is that there is not a physical process that causes this to happen. But I can try to explain what is going on:

1. Every particle has a certain amount of energy. If you have enough energy in an area then you can create that particle.

2. The Heisenberg uncertainty principle tells us that quantities that we think are absolutely defined, like time, energy, mass, speed, etc. actually have some uncertainty associated with them. In our every day lives this is not noticeable at all, but on the tiny scale of particles this is extremely important. This means that particles don't have a definite mass, but given their speed they could be any mass in a given range.

When we combine these two, we find that given particles with some energy actually can exist with a range of energies for any given short amount of time. There is some probability that for some duration these particles will just come into existence and then disappear.

This video might be helpful: https://youtu.be/3LyFap2aUN0?si=bTPTpvoWoRtTY6Fx

Big Bang: To really simplify things, imagine a sheet that is almost flat but has small dips. One of these dips got really hot one day and stretched physical space extremely rapidly in what we call the Big Bang. The definition of what distance between objects changes. It's like taking a balloon, putting two marks on it, and then blowing it up. The marks have a greater distance between them, not because they move but because the space between them changes. The Big Bang is just this really fast.

This video is really nice (and I love PBS Space Time in general for high quality physics and astronomy): https://youtu.be/K8gV05nS7mc?si=JZwkubTeMppp9tsg