No, this beta key will give you access to the Beta starting in 17th July 2014. The Alpha was a 'special' surprise for E3 2014 and you will have to enter your PSN at playstation.greatnessawaits.com/destiny.html i think this is for PS4 only but waiting to find out. This Alpha will be starting this weekend 12th June to 15th June and open to EU and US. Once you have registered you will have to wait to see if you are 'Selected'.
yes they are lmited, but if you made sure your supplier participated in the beta, you would have received a 9 digit code. make sure to add email@example.com to contacts, and check your junk folder as well. after the site update on the 10th, everyone who has put in a beta code SHOULD be able to log-on to their profile and select which console they want to play the beta on - this is not limited to the console you pre-ordered with either, it can be any you have (xbox will receive c odes later than playstation, as destiny have a partnership with them. It will most likely be after midnight that you can log-on and select the platform you wish to play on as this will be a MASSIVE undertaking on the bungie staff to get everything working - so expect delays people.
We are talking about amazon and yes this particular supplier is participating in this beta. Last but not least, they have not sent out their beta keys yet and will probably send it a day before, so god only knows what you are waffling about.