yes, it will be sterile. i've never had any issues with adding it directly to a fermenting beer.
dissolving it is a bit tricky. i have only used syrup that comes in pouches. what i've done is add some hot (but not boiling) water to the pouch, shaken it up, poured out some of the liquid, added more hot water, etc. in all i add maybe 3 or 4 cups of water. seems to work, i've never found a pile of undigested syrup after racking off the beer. who knows, maybe this is overkill... has anyone tried adding it directly, straight out of the container?