If I stop giving power to negative thoughts, ideas, and fears, will they eventually go away? If so, how do I stop giving them power?

Replacement strategy. Replace negative thoughts with positive ones.

Also, remember you should try to remove ALL negative thoughts.

Which means rather than saying “don’t think negative thoughts” say “what positive thoughts can I think?” or “How can I turn this into a positive thought?”

It’s like saying “Don’t think of Cheesecake.” What’s the first thing you will do after giving yourself that command? You will think of Cheesecake.

Instead, say if you find yourself thinking of a Cheesecake think of two cute kittens instead. Soon you’ll lose the desire to think of Cheesecake and be thinking of cute kitties instead because. Hey, after all they are cute and won't make you gain a ton of weight!