[narag]

300 cc should be similiar to around 800 lichess.

800 is very low in Lichess. If you can think just two moves ahead without losing pieces, you get 1000 easily.

For improving longer time controls are better.

Yes and no. There are different aspects to the game. Every variety is good for something.

After playing a lot of bullet, I win easily in blitz just because the time advantage. But the reverse is also true. After playing more slower games, my fast games get better.

And there are some parts of the game that you just need to sit down with a book and a couple of boards.