Statistics on bug food????? For birds and plants??? Do you want the whole thing dumped here in the comments? Or do you mean "do birds eat insects"? Yes. A lot.

Diets are highly species specific, but mosquitos are generally less than 3% of the diet for most birds and bats. Too small, don't fly around at the correct time of day/night, and pretty agile, so they aren't supper important for most birds and bats.

Also, usually they hatch in the billions all at once and die within a few weeks so there's a very limited amount of time that they even can be preyed on as food. Their strategy (many of them, not all species) is to overwhelm any predators with numbers.