When viewing an instance's main page in a web browser, scroll all the way to the bottom and click on "Instances". That will show all instances federated with, or blocked by, the given instance.

I'm not sure I can answer your other questions, though you might be interested in https://fba.ryona.agency. It will let you enter an instance and see who is blocking it. For example, here are the instances blocking my home instance, sh.itjust.works: https://fba.ryona.agency/?domain=sh.itjust.works

You can see the list of federated instances of each instance at https://example.com/instances

You can also get that data in json format by using https://example.com/api/v3/federated_instances

https://lemmy.readme.io/reference/getfederatedinstances

Mastodon and Lemmy are both using the ActivityPub protocol (Lemmy uses some extensions to federate downvotes and some other actions) to communicate between instances, but the API to interrogate a Mastodon, Lemmy, PixelFed or kbin instance will be different.