There is no example of a positive mutation. What is more, evolutionary theory does not rely on positive mutation, the concept of it doing so is far outdated.
The example that you give with the man losing his hands defys one of the fundemental precepts of biology, acquired characteristics are not inheareted. If you take a mouse, cut of its tale, and its childrends tales, and its childrens tales and so on and so fourth, mice will still be born with tales, because the change does not take place in the genetic code of the mouse, which is what the mouse passes down to its chldren.
How does evolution work then? The simple answer is variation. Your genteic code is slightly diferent from mine, even though were are in the same species. Your code may make you taller or shorter, lighter or darker, more or less muscular etc. This comes from the minor variations we have in our geens. In fact, my geens are difernt from my parants, this is not mutation, it is just the way things are, slight variation.
If you say the giraf was once a horse that had to crane its neck to get to high leaves, and its longer neck was passed down to its chldren, you would be wrong, but if you say that some horses were born with longer necks and some with shorter necks (as is true now) and that the horeses born with longer necks were slighly more likley to survive (even though a slighly longer neck is no more a mutation then being tall) and that over many generations the longer necked horses were more sucesfual at breeeding becaus they had more energy, and the subsequent generations had longer necks because their faterhs had longer necks in thier geens, and if this went on for millions of yeas, you can get a giraf.
A mutation is a sudden change in geens, and subsequently is unlikely to survive and even less likely to breed. Even if it does have the good fortune to breed, its ofspring will problably be steril. A mutation is a flaw in the genetic code, evolution is the gradual selection of the natrually occuring variation within a species.
In the bacteria example, some of the bacteria happend to have higer resistiance to the drug (just like my familly has a history of strong imune systems). Those who had a higher tollerance lived, others died. High tollarance geen was pased on, whilst other geans were not. Had the antibiotics not been administered, the sliglty more resistant strain would not be selced over the otehr. If this happens over generations, weedig out only the most imune bacteria, you eventually get bacteria that are compleetly imune (a generation takes about twenty miniutes, depending on the bacteria, so a week of antibiotics is a long time to evolve). However, if you kill them off the first time, there are no survivers and so no evolution.