Actually both ways are acceptable. First phrase is built as if it is going on right now, and the correspondent broadcasts the reportage. It may be a stylistic figure.
пожимает-обнимает-желает or пожимал-обнимал-желал or пожал-обнял-пожелал, all ways are acceptable but it should be in the same manner as all of the article, otherwise it will be crazy.
Yes, actually it is the same root as in "иметь", it has very many different applications. Compare to понять, занять, отнять, принять, нанять, перенять, донять, унять etc. etc.By the way обнимать - обнять seems to be a rather funny word (if I'm not mistaken) облетать = to fly around; обнимать = to take something around, and further from the same root of the German nehmen = to take.