Yes, under the standard rules. Pagat and Bicycle put no limit on which card you discard, apart from the card you just took from the discard pile. Some home games let another player call "rummy" and grab a playable discard, but that is a house rule: neither Pagat nor Bicycle has it.
Laying off is adding cards from your hand to a set or run already on the table, yours or anyone else's, as long as the result is still a valid set or run. To a 4, 5, 6 of a suit you could add the 3 or the 7 of that suit. You may not move cards between melds to make room.
4♥♥5♥♥6♥♥7♥♥
The 7 of hearts laid off on a 4, 5, 6 of hearts.
The standard rules just reuse the discard pile, so this rarely ends a round. Some players limit how often the pile is reused; in Block Rummy it is never reused. When play ends with nobody out, the player with the lowest card total wins and scores the difference from each other hand.