As @DoubleAA hinted, once a packaged product is open, and esp. if opened in a non-Jew's kitchen, many questions regarding kashrut arise.
A bag of sugar can pose a big problem. What utensils went into that bag? Was it a non-kosher utensil? In baking, perhaps, the person had his hands in a non-kosher baked mix and stuck his hand in the sugar bag? Essentially, the packaged kosher sugar is now non-kosher, perhaps. Same problem with the other items in the list. The item has to be non-opened and have a reliable kosher symbol.
Fruit is automatically OK if it is whole and non-Israeli produce. You should rinse it, and you may have to inspect it for bugs and other insects, though. I'll try to edit in a link about this, later.
According to OU (or Star K) (Have to edit in link when I find it), a closed bottle of extra virgin olive oil is kosher without any labeling. If it's open, I would question it being kosher, despite the fact that it has a tiny spout and it's not too likely that unkosher food may have fallen in to the oil. However, touching the spout when your hands have been in contact with non-kosher food and considering that the spout is usually plastic which is absorbable, MAY still make it non-kosher. That's something worth investigating a bit further.
Opened boxes of chocolate pose the same problem as the opened box of sugar. Even is every piece is whole and all the pieces are there and the chocolate is kosher supervised, you don't know who or what came in contact with it.