Can you explain me why in this sentence we use Present Simple tense even though it's lasting at this very moment?
"My mum and dad come. We have to turn off the console!"

The sentence looks wrong to me, it would sound better to say either of the following:

"My mum and dad have come home. We have to turn off the console!""

"My mum and dad are here. We have to turn off the console!""

If you were to say "My mum and dad 'are coming'. We have to turn off the console!", that would work.

But 'come' doesn't really work.

I actually got confused by this...

You would say "Here comes the bus."
But you can't say "My mum and dad come."

Am I right?

Well if it happens continuously, say every day, and you also put a place after it, 'come' could work.

Like this

"My mum and dad come home at 3:00pm every day."


"Here comes the bus works" too

However, in most other tenses, on its own it works.

"I came" works. Although it's not advised to say this

"I will come"

Both are okay.