Is there a minimum amount (salary) that a player can be paid?

Yes. The CBA contains a schedule – based on service time – that dictates the minimum salaries for players. The minimum salaries are based on the number of accrued season that the player has earned (6 or more games in one season on a team’s 53-man roster, IR or PUP). For 2012, those salaries are $390K (rookies), $465K (players with 1 accrued season), $540K (2 years), $615K (3 years), $700K (4-6 years), $825K (7-9 years) and $925K (10+ years).