Hi Arnav98,
To leave a review merchants will need to write it via the app store, there is no way to integrate this within the admin or the UI of your app.
Regarding requesting reviews from merchants you could check if the merchant has already left a review for your app at https://apps.shopify.com/my-app/reviews?sort_by=newest - unfortunately there isn’t currently a API endpoint for the Shopify app store to programatically check if a specific merchant has left a review, so this would need to be done manually. Alternatively you could set up a 3rd party service that integrates with your support system which monitors and cross-references merchants with data on the app store to identify when a merchant has not yet left a review.
Hope this helps,