1) If you're having trouble with short hop eggs while conserving momentum I would suggest double canceling your jump. To do this after you hop and reach the necessary height for the egg toss animation use your jump, as soon as you start the double jump DI in the direction you wish to drift and then immediately input the egg toss. The timing is kinda awkward at first but you should be able to do it consistently with some practice. If done properly you should be able to djc egg and retreat at the same time; with this method I would not suggest to djc towards an opponent as you are vulnerable while tossing the egg and with no jump you will die if you get hit offstage.
2) The reason you burn your double jump when tossing an egg is that you're slow on hitting the B button; you're inputing the up and then during the delay from when you pressed up and when you will be pressing B button the game registers a tap jump and then you start the double jump and then the B button has been hit and you toss the egg (now without a double jump, which is usually a bad thing) to help solve this try thinking "hit b" then "input up" this should help you prevent the unwanted double jump.
2.5) If you're getting the double jump when you don't want it like with say egg toss, depending on how you're executing your up-airs you could be unnecessarily burning your double jump on up airs (I used to do this as it was really easy to shuffle djc up airs with tap jump and delaying the A button; this works well if the opponent doesn't DI) but I would try to learn to use the c-stick in timing with the djc as when you chain up-airs if you spend time DI'ing up to input the up-air you will have less time DI'ing horizontally and when people learn to DI your up air chain you will need to conserve all of your horizontal momentum to continue this combo on better players.
