In draw poker games such as 2-7 Triple Draw and Badugi, a reshuffle can happen when players need more cards than are left in the deck.
The remaining cards and the discarded cards are shuffled together to create a new deck. The hand then continues using the new deck. This can happen more than once if necessary.
No. You can't redraw a card that you previously discarded.
In single-draw games, your own discarded cards aren't shuffled back into the deck, so you can't redraw a card you discarded.
In multi-draw games, discarded cards are reshuffled into the deck when needed. You won't be dealt a card that you previously discarded.
For example, if you fold the deuce of spades, you won't receive it on a later draw.
No. Reshuffles only happen in draw games.
In Seven Card Stud, if the deck runs out before all players receive their final card, a shared community card is used instead. It's dealt face up and is available for all players to use.