My thoughts.
For Abandend carts , you will get "abandend carts recovery" feature if you are in professional plan or you can use any Free AbandendApp etc..
For auto follow up, create a empty list in your mailchimp and link that to your shopify store using chimpified app which will automatically add the new customers to your mailchimp list. so you can setup the Auto-follow-up email using mailchimp automation
For Transactional emails, shopify will allow you to customie the transactional emails as per your own design. or you can use any email customisation app like Email Template Editor or similar .
Hope this infromation may help :)