Yes definitely worth it and easy to manage / get traffic. You can even use Amazon FBA to automatically handle fulfillment of your Shopify orders.
This is definitely a good idea. Often people start with Amazon and only then move on to Shopify. You may find this guide helpful to get you started: https://amzscout.net/blog/how-to-start-an-amazon-business/
Definitely. By also being on Amazon, you can introduce your brand/products to a whole new set of customer thus widening your customer acquisition funnel. We've seen a number of scenarios where within 1-3 months of expanding to Amazon, sales volume and velocity increased >25%.
Marketplace management and pricing with Monsoon