1) yes. But the rate of infection is so very very low.
2) yes, there has. You should spend some time reading up about it.
3) breakthroughs happen. That's why the vaccine wasn't listed at 100% effective.
But how many known breakthrough cases? It's 7,525.
7,525.
How many known vaccinations?
164,000,000.
Now, that's since April.
How many reported covid infections yesterday? 150,000+.
So, let's assume (even though it's wrong) let's assume ALL 7,000 infections happened today.
That leaves 143,000 unvaccinated people getting infected.
Which group is going to produce a mutation faster? The bigger group or the smaller group?
The bigger group, because there are simply more chances for it to happen.