How high is the level of professional blitz tournaments? A GM has an elo of at least 2500, and Magnus Carlsen has an elo of almost 2900, so I think you can safely say that most games between grandmasters at a level of 2400-3000 elo. This is obviously very vague, so I think you can best describe it as: Most of the games among GM's are at a level similar to 2 chess computers, with an elo rating of 2500-3000, playing against eachother.

If you take this description into consideration, how high would the level of games be at a blitz and at a bullet tournament for grandmasters? Would they be significantly lower (like for example 2000-2400), or would a good grandmaster like Magnus Carlsen still play at a level around 2700-2800?
There is insufficient data to answer objectively. However, there are a few things that can be said with confidence:


a player's bullet rating should always be less than or equal to his standard rating, because more time allows for deeper middlegame calculations
you can't accurately predict a player's bullet rating by his standard rating and vice-versa
some chess clubs have formulas for matches with time handicap where the stronger player gets less time depending on the rating difference between his and the weaker player, but in most cases the stronger player is a strong bullet player too and wins anyway
grandmasters keep their knowledge of openings and endgames in bullet time controls
certain flawed strategies work better in bullet chess
there are many grandmasters out there who are critics of fast chess
there are many grandmasters out there who have a style incompatible with short time controls


To get the data to answer your question, you would probably need to examine a lot of games between players of similar strength where one plays standard and the other one plays bullet and see from the results if you can consistently find the rating gap, and there aren't many volunteers for that.