Can I choose myself if my pension will move to the new rules?

You cannot choose this yourself. Your pension moves to the new rules. Your sector or employer has made agreements about this.

Will my pension go up or down every month?

Are you not retired yet? Then your personal pension pot moves with the economy each month. If the economy does well, your pension pot grows. If the economy does badly, its value goes down.

Do you receive a pension? Then you receive the same amount for a full year. At the end of each year, we set the amount for the next year. That amount then stays the same for a whole year, just like now.