A "picnic hamper" or "picnic basket" is a big basket that you use to carry food and supplies for a picnic, that is, a meal eaten in a natural setting away from home, such as in a park or a forest.
A routine danger of bringing food to the wild is that wild animals will want to steal your food. In the United States, the idea of a bear raiding a campsite or picnic to steal the food is very common in popular culture. I don't know how often it really happens, but it certainly does happen.
So: Would you want a bear to guard your picnic basket? No, because rather than protect your food, he would likely eat it himself. So he's saying that the Poles don't trust Russia, any more than they would trust a bear to guard their food from wild animals.
There's a very common idiom in English, "leaving a fox to guard the henhouse", that expresses the same idea.
Russia is often represented as a bear. I'm not sure if the writer chose a bear here for that reason or if that's just coincidence.
As to the last sentence: "Fracking" is a process for extracting oil from shale deposits. To "turn something on its head" is an idiom meaning to totally change it, to make it the opposite of what it was before or at least very different from what it was before. The idea is like turning a person over so that he's standing on his head: he's upside down. So the writer is saying that when extracting oil from shale deposits really gets under way, this will radically change Europe's energy market.