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Open the Shop in the game and tap "Restore Purchases" at the bottom. If you're signed in with the same Apple ID you used to buy, everything (Remove Ads, cosmetic Lily outfit, energy packs) comes back within a few seconds.
If you signed in with Apple, your save is in iCloud and survives reinstall. If you played without signing in, the save is local only and is lost when you delete the app. You can sign in any time from the Profile screen.
iOS Settings → Magic Merge → Notifications → toggle off, or leave only Daily Quest reminders. Lily's in-game nudges (her flying to a useful merge) can be reduced in the game's Settings → Lily → "Less talkative."
Rewarded ads are already opt-in — you only see them if you tap a "Watch for +15 energy" or similar button. If you'd rather never see the option, buy the one-time Remove Ads IAP ($9.99) from the Shop. It removes both rewarded and interstitial ads forever.
First try "Restore Purchases" in the Shop — this re-syncs the entitlement from Apple. If that doesn't work, force-quit the app and reopen it. If you still see ads after that, email me with your Apple receipt and I'll sort it out within a day.