Does playing one virus from my hand allow me to get all copies from my deck?
Your initial impression is correct, when you play a virus card, you may play another copy of it from the deck onto the play area (two total).  Otherwise, it would be OP to have that many resources down at once, plus the card would likely say something like you may play 'all' copies of the card when you play it, rather than 'you can play a copy, then shuffle'