do they get the concrete blocks up that hang at the end? Do they use another type of crane to assemble them?
Yep, they use a smaller crane that sits on the back of a truck and has a telescopic arm, it only takes a few days. There's a lot of construction going on in my city and I've seen them do it.
Tower cranes assembly starts with the foundation of the crane with lot concrete blocks for fixing, then they fix the first bottom part of the crane then they fix the boom with the counter weights, when they want to extend the height, they fix a jack up machine which lift up the boom and then insert a vertical piece and so on till they reach the required height. During the first installation they use a small mobile crane and then after the crane it self lift and fix the pieces
