Can I store voice recordings to iCloud

When you start the Voice Memo app for the first time, you will be asked if you want to sync with iCloud.

If you didn't say "Yes" to it, you can activate it here:

Settings > Apple ID > iCloud. Find Voice Memo in the list and activate.

Now you save your Voice Memos in iCloud. If you have other devices, for example an iPad, you will be able to see your Voice Memos in the app, on that device too. Same with Mac.

Yes, you can store it either on Voice Memo or iCloud Drive.