1) if it is a commercial product that is unopened? then it is already clean. They wouldn't sell it if it isn't. If it is 'fresh fruit' then you should perform some sort of sanitation on it. This can be tricky because if you heat it you can drive of the very flavors you want to keep. But you said 'syrup' so I'm guessing either a fruit flavor addative or maple or honey or something. Those are good to just add in.
2) sugar v yeast.. well in general there is enough yeast in the 2ndary to take care of sugars, unless you add a lot - then you want a blowoff tube anyhow- but even with that, I racked a lambic once on to some raspberries and still enough yeast for it all, even without adding more. Generally I've put the addative down, then racked on to it (to help stir it up) although you can do it the reverse and stir it up.
If you are adding a thick syrup (maple, honey, etc) then I'd strongly suggest adding it to a cup or 2 or water (or beer) and getting it disolved and more runny first. As pure syrup, they will drop to the bottom of your fermentor and just sit there and be a pain to stir in. I have trouble with my tea and honey sometimes, don't want to consider a 1lb of maple at the bottle of my carboy and needing to stir it up. Eventaully through diffusion and yeast action, the syrup would be converted to alcohol, but it will take longer.