If a card with a Recurring Credits 3 symbol is put into play, does it get 3 credits immediately or at the beginning of the players next turn?
Immediately. If your rulebook is from the first printing, make sure you check the FAQ for updated text.
Do Recurring Credits stack, or are they capped at the amount listed? I.E. If I have a Recurring Credits 3 symbol and don't spend any of the credits for 2 turns, do I have 3 credits or 6 credits on top of the card?
You can only replenish up to whatever is printed on the card.
Can I play and upgrade on an empty server (I.E. no ICE, Agenda, or Asset)?
Yes, this is possible in general. Just be careful of any restriction imposed by the card in question, such as Research Station.