One of the best studied cases in fossil record concerns evolution of horses.The evolution of horse started with Eohippus during Eocene period.It involved the following evolutionary stages:
(i)Gradual increase in body size
(ii)Elongation of head and neck region
(iii)Increase in the length of limbs and feet
(iv)Gradual reduction of leteral digits
(v)Enlargement of third functional toe
(vi)Strengthening of brain and sensory organ
(vii)Increase in the complexity of teeth for feeding on grass
 Eqquus(Plestocene period)
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 Pliohippus(Pliocene period)
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Merychippus(Miocene period)
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  Mesohippus(Oligocene period)
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Eohippus(Ecocene period)

Yes,a natural disaster can be cause for extinction of species.As new species evolved to fit ever changing ecological niches,older species fade away.
But,the rate of extinction is far constant.In last 500 million years,50-90% or more of all species on earth have disappeared in a geological blinks.the most studied mass extinction between the cretaceous and palaeocene peroid about 65 million years the cause is suspected to be volcanic eruptions and impacts of large asteroids or comets striking the earth.

The creation and the presence of variation is directionless in regards that they occur randomly and spontaneously. The variations which are helpful in the adaption of an organism towards its surrondings would be passed on to next generations.
Natural selection is the most critical evolutionary process,which can be considered directional as it leads to only one path that is selection and prepetuation of better adapted individuals.Natural selection leads to survival of the fittest and disappearance of all those organism which do not fit in the prevailing environmental conditions.

(i) The process of evolution of different species starting from a point in a geographical area and finally radiating to other areas geography is called adaptive radiation, e.g. Drawin's finches. Darwin observed different type of beks in the same black bird in Galapagos Islands and he concluded that this was due to adaption for different situations. 
(ii) When more than one adaptive radiation appear to have occurred in an isolated geographical area and two or more groups of unrelated animals come to resemble each other for similar mode of life or habitat, it is called convergent evolution. Convergent evolution of Australian marsupials and placental mammals are example of this evolution.

The meaning of the given words are as given below
Race. It is a classification system used to categorise humans into large and distinct populations or groups
by anatomical, cultural, linguistic, geographical, historical and for religious relationship.
Breed. It is a specificgroup ofdomestic animals or plants having homogenous appearance and behaviour
and other characteristics that distinguish it from other animals or plants of the same species. They were formed through selective breeding.
Cultivar. It is a plant or grouping of plants selected for desirable characteristics that can be maintained by propagation. 'Cultivar' stands for 'cultivated variety'.
Variety. A variety arises naturally in the plant kingdom and plant grown from its seeds will typically come true to type.

Yes,  we agree. As the gene flow occurs through geographical barriers over generations, by studying specific allelic frequencies in various populations of the world, we can predict the human migratory patterns in pre-historic and historic era.
There have been projects undertaken such as human genographics project. Which uses data from studies on specific genes/chromosomes/mitochondrial DNA to trade the evolutionary history and migratory patterns of humans.

Factors affecting allele frequency in populations are described below:
(i) Mutations: These are sudden heritable changes which are supposed to be the primary source of genetic variation. They are of following two types.
(a) Chromosomal Mutations: They arise due to changes in chromosome number and changes in structure.
(b) Gene Mutations: These are changes in gene structure and expression due to addition, deletion, substitution or inversion of nucleotides.
(ii) Non-random Mating: Repeated mating between individuals of certain selected traits changes the gene frequency, e.g., selection of more brightly coloured male bird by a female bird may increase the gene frequency of bright colour in the next generation.
(iii) Gene Flow (Gene Migration): It is the movement of alleles into and out of a gene pool. Breeding of immigrants with the host population adds new alleles to the gene pool of the host population.

1. We are still not clear whether evolution and natural selection are processes or results of some unknown processes.
2. On one hand, when we describe the world as we see today, we describe evolution a process.
3. On the other hand, when we describe life on earth, we treat evolution as a consequences of the process of natural selection.

With the industrial growth in 1920, the white-winged grey-coloured Biston betularia was rapidly replaced by a dark-coloured melanic Biston carbonaria as the later had more chances of survival and favoured by Natural selection. But after 1956, the coal was rapidly replaced by oil and electricity as energy source in the industries which reduced soot deposition. So the light coloured moth is again replacing the dark-coloured moth by reverse evolution.