Hey - fellow solopreneur SaaS founder here.
I made BudgetSheet ( https://www.budgetsheet.net ) and have dealt with a few of the same issues here, so I will try my best to answer them:
1. I use License Keys for my project, which I store in my own database associated to the user account that made the purchase. LemonSqueezy allows you to send custom data with a purchase, so I send the user token with the payment link users click on from inside my app when they make the purchase. You can then get this same custom data back in a webhook, which you can use to associate the purchase with a specific user account once it has been made along with the LemonSqueezy subscriptionId. It is a relatively minimal amount of work to achieve this, and LemonSqueezy has examples for how to verify their webhook data that you can just copy and paste into your own. I am sure other payment providers are similar as well. Once that data is in my local database, it's a simple query lookup to see if a user has paid or not (be sure to also handle cases for subscription cancellation and expiration though - also webhook events!).
2. If you are worried about taxes, then you can use a MoR (Merchant of Record) payment provider like LemonSqueezy, Gumroad, or Paddle. I personally use LemonSqueezy because I liked their UI the best, and they supported license keys as part of the purchase.
Good luck with your business!