Shopify App Review - OAuth/finding the shop name

[sfyAppReview24]

I am in the process of having my app reviewed to be included in the Shopify App store. After submitting, I hit the common blocker of not immediately doing the Shopify OAuth, before logging into my web app. This leads me to several questions:

1. Do I need to have an app in the app store at all in order to use the Shopify API?

2. If yes, then how do I go about getting the Shopify Shop name/id for the oauth? I checked the POST request that is sent when navigating to my web app (the current "incorrect" flow) but I don't see the shop name in the request.

3. The emails I have been receiving list the deadline to submit my app as June 19, 2024. Since I have submitted and am in the process of fixing the problem do I have additional time or must I fix the issues by June 19 otherwise my app will be "sunset"?

Some background: I cannot go the custom app route, my app is already in multiple stores. It was previously a unpublished/private app which worked fine for our needs - only needing to access the API minimally. Currently users log into my app and do the oauth for Shopify within the app since Shopify is only one of many integrations we have.