Evolution is any change in allele frequency of a population over time. This can certainly be observed directly.
Bacterial drug resistence most certainly is evolution.
Common ancestry is so well demonstrated that it is commonly referred to as the "fact of evolution." This is due to the great number of testable, and well tested predictions of common ancestry, such as the twin nested hierarchies.
No, you appear to be the one who is confused. We can help, however.
Common ancestry is not in doubt in the scientific community. The only questions involce specifics of phylogeny and the relative merits of specific mechanisms.
Nobody has ever suggested that reptiles evolved from mammals.
Because of the gradual nature of evolution, drawing species distinctions can be difficult, see ring species for an example. This is expected.
Speciation leads to reproductive isolation. Over time, this leads to divergence, such as that between dogs and bears which share a common ancestor.
What type of bird is this?
Actually, it isn't a bird, despite its feathers. It is a dinosaur. A dromeosaur, to be exact. Here is a nice closeup of its proto-feathers.