Does this mean when Doha was asking about the game... He remembered all of it? Or was th...

Yep he does. He was just interrogating Bada, the experimental NPC, how much he knows about the game and much he's done so far

1. To be honest, I don't quite understand how cassettes work at this point. I understand that Doha was an NPC in the first episode because Cousin uninserted his cassette, and we see his real personality, it's a NPC without any memories yet.

2. In the next episode, when Doha plays along with Bada, he inserts a random casette and removes Cousin's. When Doha inserts it, does he remember everything? Is it enough to save a random cassette to remember again or do you have to have a custom one?

I think he inserted...his??

2. He will remember everything again in the next game. Similar to HyungShin (tape removed) and Yongtaek (tape inserted), they will gain/lose their memory on the next gameplay

HyungShin: https://www.mangago.zone/read-manga/dreadful_night/uu/br_chapter-185119/pg-1/
YongaTaek: https://www.mangago.zone/read-manga/dreadful_night/uu/br_chapter-252619/pg-1/

Here's an explanation of how the cassete player and save system work: https://www.mangago.zone/read-manga/dreadful_night/uu/br_chapter-253924/pg-1/