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Collections are a way for you to organize kata so that you can create your own training routines. Every collection you create is public and automatically sharable with other warriors. After you have added a few kata to a collection you and others can train on the kata contained within the collection.
Get started now by creating a new collection.
after solving each kata, click on attempt button on bottom right corner of your screen.
if your solution passes all the test cases, the submit button automatically appears.
Maybe have a look there: https://docs.codewars.com/getting-started/solving-kata
It's better if you ask this on CW discord, but essentially yes. You simply click 'Train' and complete the function in top-right window.