Homologous
a.Humans and dogs share ancestry. Human and dog share homologous structure in their arm. (Human's and dog's forelimb) The function of both species' arm and wing are totally different, however, you can see that their bone structure is very similar. They are evolved from the same front forelimb structure.*1
b. Even Humans and dogs has very similar bone structure and same number of bones in their forelimb, their forelimb has different external features and function. Humans and dogs are relatively closely related species, and they likely share over 90% of their genes.*2
The difference in appearance of their forelimb bone structure is that humans have longer fingers than dogs' forelimb, and the functional difference is clear that human can grab things by using the fingers and dogs cannot. These difference is evolved by natural selection. Evolutionary change occur the difference in their genes, and it appears as the difference in the function of their forelimbs.
c. Their last evolutionary common ancestor is fairy unknown, however, scientists believes that is rat. The rat is called Protungulatum donna, it is the common ancestor to all mammals.*3
Analogous
a.Sharks and Dolphins has very similar appearance and shapes, however, they are analogous traits. Sharks are classed as fish. and dolphins are Mammals. They are evolved independently, and they are likely coming from separated branches of the phylogenetic tree.
b. They have many similarity in there shape such as fin, dorsal pectoral fin and flipper, and torpedo-shape. And the function and purpose is almost same. They are alike because they live in the same environment: sea and ocean. Dolphins migrated to the ocean after sharks, dolphins are evolved to this way as natural selection for the life of ocean predator.*4 The evolutionary change dolphins experienced was converging evolution.
c. No. Because even Sharks and Dolphins had shared common ancestor in the tree of life, it is too far and will not be considered a recent common ancestor.
Image
http://thevoltagegate.blogspot.com/2006/07/why-spiders-arent-insects-iv.html
http://evolution.berkeley.edu/evolibrary/article/analogy_04
Resource
*1 http://science.jrank.org/pages/348/Anatomy-Comparative.html
*2 http://www.newton.dep.anl.gov/askasci/mole00/mole00286.htm
*3 http://www.nytimes.com/2013/02/08/science/common-ancestor-of-mammals-plucked-from-obscurity.html?pagewanted=all&_r=0
*4http://evolution.berkeley.edu/evolibrary/article/0_0_0/analogy_04

