Hello! welcome to the community. Good news! you can do all of this with Zapier. Here are some comments/resources: 

New client

• Email template X is automatically sent out to the client.

  • Yes you can do this with various mail apps like Gmail/Outlook etc (The action would be "Send email")

  • Here's a helpful resource, too: https://zapier.com/help/create/email-and-text-messages/send-emails-in-zaps

• 1 day after the start of the plan an Email/text is sent to me telling me what I need to do next.

  • Yes - You can do this by using Zapier's delay functionality

  • Here's a link: https://zapier.com/help/doc/how-get-started-delay-zapier

• 2 days after the start of the plan an Email/text is sent to me telling me what I need to do next.

  • Yes, you would just add a new delay step as per the above

• If the above is possible. Then can some more of the following items be programmed?

Existing Client

• Can I edit an email template before it sends so I can personalize in

  • Yes. Instead of sending the email from Zapier, you would create a draft in your outbox

• Can the plan be paused if the plan item before it has not been completed yet?

  • Yes - You can set up some logic, I imagine - I'd just need to know a bit more about how you're managing the items.