I can only speak for prints from my Canon Selphy 710 Dye Sub printer so
Are they ok to use for stuff like Key rings and magnets? Yup but you do have to use the special paper, so prints need to be trimmed and then stuck onto or into the magnet or keyring.
Is it all right for the paper the be trimmed with no problem? Yup.
What about cost effective? Is it more expensive than the ink jet ones? Using 7dayshop as the supplier for the paper/ink packs for the 710 (£25.99 for 108 sheets), prints work out at just over 24pence each (gone up a bit since last time I bought some when it worked out at 17p/print) which is a bit more expensive than home printing 6x4 prints on a home inkjet.
The biggest advantages (for me) of the dyesub printer are the size (easily small enough to pack into the hold luggage even with extra paper and inks, packed in its own carry case) and the fact that the inks cannot escape into the rest of the luggage. Another thing I like about the Selphy paper is that it's pre-printed with postcard layout lines. The 710 also comes with card slots and is also PictBridge compliant, so I can either shove a card in the slot or connect the camera to the printer.