As regards "than" usage...
"This also applies when the second clause or phrase is elliptical: He's taller than I."
and
"But when "than" occurs with a pronoun in the objective case, it's a preposition: He's taller than me."
So both usages are correct?? That just doesn't sound right.
Both usages exist. It's not clear what it means to say that a common grammatical construction is "incorrect". Some people mean something like "educated speakers rarely use this construction". If we use that meaning of "incorrect", then sentences like "He's taller than me" are not particularly incorrect: they're widely heard from educated English speakers.
Other people mean something like "I have been told that this construction is wrong (e.g. by my elementary school teacher, or by the author of some book about 'common errors' in English usage that I have read" or "this construction offends my sense of logic or neatness". If we use that meaning of "incorrect", "He's taller than me" may be incorrect, depending on which "authorities" you follow or which principles of logic or neatness you find convincing.
This is quite a popular grammar question. Here is an excerpt from the classic Chicago Manual of Style:
The case of a pronoun following a comparative construction, typically at the end of a sentence, depends on who or what is being compared. In My sister looks more like our father than I [or me], for example, the proper pronoun depends on the meaning. If the question is whether the sister or the speaker looks more like their father, the pronoun should be nominative because it is the subject of an understood verb {my sister looks more like our father than I do}. But if the question is whether the father or the speaker looks more like the sister, the pronoun should be objective because it is the object of a preposition in an understood clause {my sister looks more like my father than she looks like me}. Whatever the writer’s intent with the original sentence, and regardless of the pronoun used, the listener or reader can’t be entirely certain about the meaning. It would be better to reword the sentence and avoid the elliptical construction.
Also, this may be even more helpful:
If a pronoun appears in a prepositional phrase, the pronoun is usually in the objective case {with me} {alongside her} {between them} But note that than may function as either a conjunction or a preposition {he’s taller than I [am]} {he’s taller than me}. In edited English, taller than I has predominated over taller than me in American English from its very beginnings, and in British English it predominated until the 1990s. Throughout the literary history of Modern English, than me, than her, etc. have been regarded as less polished (to say the least) than than I, than she, etc. That is to say, in formal registers than (like as) is considered a conjunction, not a preposition. But in spoken English, than and as are often treated as prepositions that take a pronoun in the objective case {you’re better than me} {you’re as well known as me}. A possessive pronoun may be used before the preposition’s object {to my house}.
In short, than I considers than to be a conjunction, and it is viewed today as being formal. Than me holds than to be a preposition, and is accepted as standard in informal spoken English. (This also means that modern spoken English views than as a preposition and not a conjunction.)