Can Ads Manager change my ad budgets without asking me?

Only if you allow it. Go to Marketing → Ads Manager → Settings. Under What may Ads Manager do on its own? you can choose:

• Ask me first: it never changes a live ad by itself.
• Pause automatically: it may stop ads that waste money.
• Autopilot: it may also raise budgets and turn ads on, but only within your limits.

You can also set a Daily spend cap (required for Autopilot), a Largest budget change (%) and Wait between changes (hours). The kill switch stops all automatic changes at once. New campaigns are created paused until you press Launch.