Sourdough Starter

If I have an active sourdough starter (yeast culture) that needs to be fed every 5 days with flour and water, do I let it die over Passover or can it be fed?

It is chametz so you can’t own it or have anything to do with it once Pesach arrives.

Can a sourdough starter (yeast culture) be fed (throwing some away and adding more flour) on Shabbat?

If not, please explain the melachot that prohibit it. Thank you.

I don’t know what that is, but you can’t do anything on Shabbat for after Shabbat. “anything” includes any action. Talking is dependent on specific subject matter