How does the process of attaching NS to another provider's domain work?

Question

Domain Name System

Given two DNS services, suppose sales.domain.com and panel.domain.info
The first service (sales.domain.com) sells domains at good prices, the second service (panel.domain.info) offers a convenient domain management panel.
Let's say domain.xy was purchased from sales.domain.com.
Step 1. In the domain control panel, NS records are made to the panel.domain.info server.
Then I try to check NS records via DIG and get an empty response.
Step 2. In the panel.domain.info control panel, I attach the domain.xy domain.
I try to check the NS records via DIG and receive the panel.domain.info server's NS in response.
Question 1. Why after changing the NS servers in the sales.domain.com service does dig respond with an empty response? Doesn't sales.domain.com fit NS into domain.xy ?
Question 2. What happens when panel.domain.info tries to propagate domain.xy to its service? Does it make a request to check NS and if NS match then attach? If not, what is the mechanism?
Question 3. Is it possible to use dig to check which NS are in sales.domain.com if they are not already attached to panel.domain.info ?