Is zakat due on the full amount (6,000 Riyals) or on only 3,000 Riyals, knowing that 3,000 of it is an unpaid debt, and the money is saved in the bank and being spent from? And is it a condition for the entire amount to have completed a full year (hawl)?

For Zakat to be obligatory on wealth, it is a condition that the wealth reaches the Nisab (85 grams of gold or 595 grams of silver), and that a full Hijri year passes over it. If the accountable person is not certain that a full year has passed over the wealth, then Zakat is not obligatory on him, because the default is the exoneration of one's liability and the absence of obligation until proven otherwise.