Why are the children fearful of the Professor at first, and how do their feelings change?

The children are indeed scared of the Professor at first. But then, most people in their situation would be. He comes across as a really unfriendly man, kind of creepy in a way—certainly not the sort of person you'd want to get too close to. It's no wonder that children in the neighborhood stay away from his shop. The Professor's been turned into the local bogeyman, a figure of legend rumored to be responsible for not one, but two child murders in the vicinity. If this guy turns out to be anything other than a stone-cold psychopath, it'll be a miracle.
But miracles do happen, and over the course of the book we find out that we—and the children—have been getting the Professor all wrong. It turns out that his lack of engagement with the outside world isn't because he's a serial child killer, but because he withdrew into himself after his wife passed away. The death of the Professor's wife was so painful to him that he didn't want to get too close to anyone else, and so he retreated behind closed doors, cutting himself off from the neighborhood.
Now that they've seen a whole different side to the Professor, the children's feelings about him change accordingly. They learn to trust him, seeing him as one of life's good guys. He demonstrates this when he saves April from being attacked in his storage yard, and also when he gives the children the keys to the yard so that they can continue to play there.