1) Credit Card/Paypal Gift Limit: Gifting with Credit Card/Paypal is disabled on new accounts. The restriction will be lifted 3 months after you make purchases worth $10 / €9.19 / £6.69 / A$13.99 / 719.00 RUB / 55 DKK / 70 NOK / 65 SEK / 30 PLN / C$10 / 10 CHF / R$32 in total.
2) Gifting restriction/day. You may not purchase the same game as a gift more than 1/day.
3) You may not make more than 5 gifts/day (to be honest, I'm not sure if this restriction is still valid).
I seem to remember hearing that you might be able to get the "buying x gifts per day" restriction at least temporarily lifted by contacting Support about it. Somebody was collecting gifts during a sale to use for giveaways later, and contacting support did the trick. It has been awhile, so I might be mis-remembering some aspects of this.
Based on my own experience, they won't allow accounts to buy gifts without hitting that "money spent" threshold.