All of your questions' answer is YES.specs on the LED string..
does it already have current limiting?
Is 12V the Vf of the LED or the operating voltage of the strip.
More than likely the LED strip already has current limiting so any regular 12V "wallwart" could be used provided it has more than a 500mA output capacity.
You just need to buy one of these if you don't already have one laying around your house..SMPS is much complecated to me... actually I am not very well in power electronics... I thought that there may be another simple way to acomplish this kind of job. Once I saw a tiny 12V power supply that converts 220V mains to 12 VDC @ 1amp. that was a professional tool and used few components... doide, transistor and a small roomed transformer as far i remember.
by Aaron Carman
by Duane Benson