If birds are dinosaurs, then are mammals reptiles?
Reptile is not a clade - it is a paraphyletic group because it does not contain all descendants (i.e. birds) of a common ancestor. Humans are amniotes like birds and reptiles but while birds and reptiles are sauropsids, mammals are synapsids. Humans are not amphibians either because amphibia is another paraphyletic group which is distinct from amniotes. Possibly some amphibians and amniotes share a common ancestor. Amphibians, sauropsids and synapsids can be grouped together under tetrapoda. So both humans and frogs are tetrapods but humans are not amphibians.

However, birds are dinosaurs and belong to a very specific sub-clade of dinosaurs called theropods. Both dinosauria and theropoda are monophyletic groups - i.e. they contain all the descendants of a common ancestor.

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Extending this to bacteria. Yes you would group all living things (eukaryotes and prokaryotes) and can call them cellular living organisms.
However, animals (or any other eukaryotes) are not bacteria (they have diverged a lot). Moreover, extant bacteria are not precursors for all life. The precursor is called Last Universal Common Ancestor but we don't know much about it (at the moment it is a hypothetical organism). Eukaryotic evolution itself is a big mystery. So it would be  preposterous to call all lifeforms as bacteria.