So, we are in Phase 2. I have already opened. It is my turn again. On the end of the run is a 10-card. I am about to play an 11-card but realize I haven’t picked a card yet. On the top of the discard pile is a 12. I picked that card up and played that with my 11. (I thought picking up the 12 would be safer than getting some random card I might not be able to play). One of our players flipped out saying that was an illegal move I did and carried on for a few minutes until he ruined the game and ended the game by throwing the cards across the room. So, I ask, was it a legal move or not?
Perfectly legal. There is no limit to the number of cards you play onto sets or runs on your turn (assuming you have made your phase and unlocked the ability to do so) and there is no stipulation that the cards you use must have been in your hand before the start of your turn.
On your turn, you complete the steps in order: Draw one card (either the top face up card from discard pile as long as it isn't a skip, or the top face down card from the deck), Make your phase (if you haven't already using any cards in your hand), Play additional cards onto your or another player's sets or runs, Discard a card (, then check if out of cards to trigger the end of the round).
The cards used by you during your turn may be any card currently in your hand at the time of wanting to play the card, and that includes the card you picked up during the first step.
As an amusement, you can even run out of cards before the discard phase, having played the card you would otherwise have discarded (though there is no benefit to doing so apart from gloating).