yes you can publish theme and remove password that go to live
Hyde here from Shopify.
For your store to be available there are a number of factors that need to be in place:
1. Are you on a paid plan with Shopify? You can double-check that by going to Store Admin > Settings > Plan. If not you will have to pick a plan before you can make your store live.
3. If you're using a third-party domain, make sure you've connected it properly as per our guide.
Could you let me know what the error message is that you're seeing? And could you confirm that everything listed above has been done and is set up correctly, please?
I look forward to hearing from you!
All the best, Hyde.