How high can something be released and still fall back to earth? At what point is something outside of the earth's gravitational field?

There is no distance that gravity has zero effect. The gravitational field of the atoms of the Earth fill the entire Big Bang universe.

But - The universe inflates at the rate of roughly 70 km/sec per megaparsec. This introduces an interesting math problem. The gravitational force of the Earth is 9.8 m/sec^2. Gravity falls at 1/radius^2. At what point has the inflation of the universe exceeded toe gravitational force of the Earth so an object dropped will move away forever? The real puzzle of that problem uses the mass of our galaxy not the mass of the Earth but the equation remains the same.

Incidentally, that is a problem that Einstein worked on until his dying day. Is the mass of the universe balanced so that it expands forever or that it will eventually collapse? Einstein could do the math for our planet and get an easy anwser but the mass and size of the universe are still not know well enough to answer.

Q1. No limit if you ignore other astronomical objects which could pull the object towards them.

Q2. The point you are outside earth's gravitational field is 'infinity' - an infinite distance from earth.. So you can never be totally outside the earth's gravitational field (though it may get too small to detect).

the gravitational field goes on forever.

but you do get to the point where other things will have bigger effect

if you go toward the moon 174,000 miles from the earth

and toward the sun it is

160,725.935 miles.

According to Google, about 6378 kilometers for the gravitational field