States are situations that happen or last for some time without interruption. For that reason they are thought of as permanent situations.
If you possess something you possess it night and day, without interruption regardless of whether you're using that possession at the moment or not. For example, I have a guitar. I'm not playing it now but it is still mine.
If you believe in something, you believe in it without interruption. I believe in God. I believe in God all the time, even when I'm not talking about him.
That is why stative verbs are not normally used in continuous tenses. Continuous tenses are more natural with Dynamic or Action verbs. They are more temporary and can be interrupted at will. They can be imagined in progress.
I am typing this text.
You want to know whether get and become are stative verbs or not. Well, we use these verbs to talk about change. They are temporary.
You can say: I'm getting nervous or I'm becoming nervous.
They are not stative verbs.