Selective and existential unforgability of signature schemes
1) In the selective unforgeability game (often also denoted universal unforgeability), the adversary is given the public key and a target message for which it needs to produce a forgery (instead of giving the adversary only the public key and letting the adversary choose the target message). 

2) No, any scheme that is EUF-CMA is also SUF-CMA (this is easy to show; build an EUF-CMA adversary from any SUF-CMA one by simply running the SUF one on an arbitrarily chosen message).