Both 1.e4 and 1.e3 are legal on move one. Play 1.e3 and that pawn will never reach e5 in a single move again, because the double step belongs to a pawn that has not yet moved, and it is spent the moment the pawn touches e3.
What surprises people is that the right does not run out. A white h-pawn that has been sitting on h2 while forty moves happened elsewhere can still play h4. It is not a first-move-of-the-game rule, it is a first-move-of-that-pawn rule.
Both squares have to be empty
The pawn cannot jump, so anything standing in front of it blocks the double step as completely as it blocks the single one.
h 1 That is a real technique, not a curiosity. A knight or a bishop parked directly in front of a pawn stops it dead, which is what blockading a passed pawn means. Note also the square the pawn crosses: with a piece on e3 there is no e2-e4, and with a piece on e4 and nothing on e3 the pawn can still play e3.
This rule is the reason en passant exists
Before the double step was introduced, a pawn on e2 had to walk past e3, where a black pawn on d4 or f4 could take it. The faster rule let pawns slip past enemy pawns untouched, so a second rule was added to close the gap: if a pawn uses the two-square move to run past a square an enemy pawn attacks, that pawn may capture it as though it had moved one square.
So the two-square move and en passant are a matched pair. White pawn on e5, Black plays d7-d5, and White may answer exd6 on that turn and no other. The precise conditions are on the en passant rules, and there is a set of en passant puzzles worth ten minutes, because the move is easy to understand and very easy to forget in a real game.
Which is the practical point. When you play a double step past an enemy pawn, look at whether it can be taken before you let go of it. And when your opponent plays one past yours, look before you reply with something else, because the chance disappears the instant you do.