Venecol is right about PS players. They are UFA's. They can't be "claimed" by another team but other teams can certainly make offers. ("Claims" are made during waivers but if a player is on the PS, he has cleared waivers). There is, however, a restriction that you can sign a PS player of your upcoming opponent.
While a PS player can count against the salary cap, I don't know of any example where they actually did because they would have had to have been in the top-51 of that team's salaries. I can't say 100% for certain it has never happened, just that I sure can't think of anything.
I also don't know of any examples of a player choosing to stay on one team's PS when another team was willing to put him on the 53-man roster. Quite honestly, I doubt such a thing has ever happened but I can't say I know for certain.
Here is the relevant CBA section:
Section 2. Signing With Other Clubs:
(a) Any player under contract to a Club as a Practice Squad player shall be completely free to negotiate and sign a Player Contract with any Club at any time during the League Year, to serve as a player on any Club’s Active or Inactive List, and any Club is completely free to negotiate and sign such a Player Contract with such player, without penalty or restriction, including, but not limited to, Draft Choice Compensation between Clubs or First Refusal Rights of any kind, or any signing period, except that such player shall not be permitted to sign a Player Contract with another Club to serve as a Practice Squad player while under contract as a Practice Squad player.