I have bought Xbox Game Pass Core but I can not install games from game pass

What games have you tried installing? Keep in mind, Core has a small amount of games compared to the other levels of Game Pass.

Game Pass Core does not include all of the same games as Ultimate. Ultimate includes all games from Game Pass for console, PC Game Pass, and EA+ games. Game Pass Core is mainly for the ability to play online multiplayer and includes about 25 console games. So unless you've bought the games you're trying to play, you won't be able to play them unless they're one of the handful available with Core.

They haven't changed the price. They will include at launch of the new Game Pass Core, 25 Xbox Game Pass games for you to play, and more games will be added sometime in the future. They also will not be taking away any Games with Gold you already have claimed.

More info on Game Pass Core can be found here https://www.xbox.com/en-US/xbox-game-pass/core

I have recently bought game pass ultimate when I had game pass core with 11 months remaining but it did not convert over and was cancelled. And I can no longer get it back along with ea access. What should I do

If you have been playing DayZ on Game Pass Ultimate, then when you downgrade to Core, the game is not included. You will either have to purchase the game, and then you will be able to play online with Game Pass Core, or purchase Xbox Game Pass or Game Pass Ultimate to continue playing the game from there.

On another note, you do not need a subscription to play online multiplayer on the PC.