There are two ways of looking at ToE. The objective evidence and the evidence that is supportive of the theory.
The objective evidence is of course that which can be observed, the reproducibility of the evidence, and tested. This included studies such as determining environmental factors on genes and can be shown in animal breeding.
The second is historical evidence. This can not be tested in an objective manner since it can't be tested, reproduced or observed in its own time. This second area of ToE has evidence that is supportive of the theory. This is where common ancestry comes in. Genetic similarity is something that is used to support the theory.
This is incorrect. Historical sciences can be tested as well as any other kind of science. Evidence does not have to be "tested in its own time" or else (for example) geology, astronomy paleontology, archeology, and a fair amount of physics would not be sciences. For any hypothesis or theory be science, it must be able to be tested but there are a number of ways of doing this scientifically.
With the "historical" sciences, testing is usually done in some form of look over there and you will find thus. This is what was done with Neil Shubin finding Tiktaalik roseae. The TOE suggested that this kind of fossil would be found in a certain type of formation and Shubin went there and found Tiktaalik.
The same with archeology, a prediction can be made that in ruins of a particular type of culture certain artifacts will be found and others will not. The scientists go there excavate and see how well their predictions work out.
The idea of splitting science into two types in this manner is advocated by Answers in Genesis but few if any scientists agree with them. All science uses the same process. There are considered to be two general classifications in science but it is more along the lines of "experimental" (Ham calls this observational science) and historical but with no clear dividing lines.
Something to go along with this: What is reproduced are the observations not necessarily the event. How could you research stellar physics if you had to reproduce a sun forming in the lab? What is reproduced and studied are the recordings made of stellar events. The observations are the evidence and they are often observations of events that happened millions of years ago. The same principle holds true for geology and all the rest.
For an archeologist to work by the "in its own time" restriction means they would have to replicate the culture they are studying people and all. No, in archeology, the artifacts are the observations and those are studied in the here and now.
While techniques vary, all science works the same.
Dizredux