First of all, it has been several years since I had my organometallics. I'll try to provide some understanding of mine.
The first question I would search alkene migration as the key words. I would guess this migration is caused by the intermediate in which the lithium is attached to the oxygen, which eventually leads to the Z conformation of the double bond in the product.
The second one I would do the synthesis by attaching hydroxyl chain first. The acidic hydrogen on alkyne should make this reaction feasible. Then, under basic condition, the hydroxyl gourp will lost a proton, which could be able to occupy an empty orbital of the copper atom in the catalytic cycle. In this case, the addition of the activated alkyne could only happened though the open site.
The third one is from a reported literature. You can read the literature and understand the catalytic cycle of this reaction. check the link below.
http://sci-hub.tw/http://pubs.acs.org/doi/10.1021/jacs.5b08914