This gets into colloquial speech, which is much less regulated by style, but of the style guides that allow contractions, do any allow constructions like “Frank’s an alright guy?”
I have to admit that it’s a little confusing and when I see it I reflexively see a possessive, but in principle it shouldn’t be any more or less confusing that “the school’s doors” vs “the school’s a massive success” which seems like fairly standard writing to me.
Yes of course it is. Only aliens in films talk without using possessive pronouns. When writing it is more a matter of style; if you are writing speech in a novel, it would be normal; if you’re writing an instruction manual - less so.
I can never remember all those rules and just go by what looks and sounds right.
Well, of course you can use it and be understood, but that’s a pretty low bar.
I was mostly wondering about what actual style guides that allow contractions say. (Since style guides are just enforcers of consistency among a community). It just seemed slightly ambiguous to me in a way words like “that’s” isn’t.
If you’re following a style guide, then by definition you are writing in a formal context, and would avoid contractions in general. But any style guide will also tell you to quote spoken words as faithfully as possible, so if someone said it, you can use it in a quotation.
That’s not true. Neither MLA nor Chicago Manual really care about contractions, they offer advice but they don’t prohibit them.
Whatever. The general rule of thumb is that you should avoid contractions in formal writing, but they are ok in less formal contexts, especially if you are going for a ‘conversational’ feel. There is nothing special about proper nouns in this regard. Perhaps pronouns are a bit special in that it is probably acceptable to use a contraction with a pronoun at a somewhat higher level of formality than than it is with a noun.
No, it’s not OK. “Alright” isn’t a word. It’s “all right.”
Then, can you say “Alright’s not a word”?
According to my dictionaries, it’s not OK, but not for the reason you indicated. It is an accepted spelling variant for “all right”, but it is an adverb, and only for that reason can it not be used in “Fannk’s an alright guy”.
Alright != all right.
Alright is a word frowned upon by some pedants in some contexts.
What are those contexts? In formal writings.
What is formal writing? Now we’re in for a long, juicy, unresolvable, and eventually mean-spirited battle about impossible definitions.
Today I’d say that formal writing is a vanishing field, limited mostly to a few technical and academic applications. Here’s one definition:
Most ordinary communication, even by professionals, is not concerned with this level of formality. Books, newspapers, magazines, whether in print or online, use a style that I call “good writing,” a mixture of formal and informal aspects that depend on the subject and the context. Good Writing in this sense is what good writers do - somewhat circular, but far more relevant to almost everybody’s lives outside of academia. Good writers care more about accessibility, understanding, and pleasing an audience than they do about the formal strictures of academic prose - which is often and rightly lambasted for its unreadability.
Style guides don’t care much about tone, and that’s really what the OP is asking. There’s no question that the Frank’s in “Frank’s an alright guy” is perfectly acceptable in almost any application of good writing. Alright is more questionable, but still used so widely today that only pedants would blink at it. Google gives “alright” 34,400,000 hits and “all right” 94,600,000 hits. I personally don’t like alright and don’t use it. I gave up denigrating it years ago, nonetheless. Usage changes constantly, and the entire trend of language use is toward the less formal. Formal writing should be limited to the least possible number of specialized uses, because it’s a pain to write and a trial to read.
I’ve never heard of a context where one would be ok with “She’s six feet tall” (or whatever) but not “Frank’s six feet tall”. This seems to me a purely hypothetical objection; what makes you think anyone would object, other than the untenable principle that no one ought suffer any momentary parsing ambiguity anywhere?
Dave’s not here, man.
Someone had to say it. 
I guess this makes me a pedant, but I hate, hate, hate the idea that if a certain number of people misspell a word for a certain number of years, it then is rendered acceptable to do so, and entered into dictionaries as such. I would guess there are millions of examples of people conflating “they’re” and “their”; does that mean it will become acceptable to make those spellings interchangeable?
If you are quoting someone, it is all right. Moreover, that’s a colloquial phrase and is commonly used that way.
…and Bob’s your uncle!
No, because the good writers as I defined them don’t commonly make this mistake.
Usage changes when good writers adopt the new usage, not when poor writers do. The use of apostrophes in plurals won’t be entering dictionaries, even if 100,000,000 people get it wrong.
I feel ‘alright’ will earn a place in the lexicon because it does not have the same meaning as ‘all right.’
“How was the test. Fred?”
“My score was all right!” or “My score was alright.”
Yes, exactly. It is not (now) a misspelling at all (although perhaps it originated as one), but a semantically distinct word that not only means something quite different from “all right”, but is pronounced subtly differently. If something is “all right” it is perfect, ideal. If it is “alright” it is acceptable, or just barely satisfactory.
In my opinion, “alright” has long since “earned” its place in the lexicon. It is a commonly used word with a distinct meaning, and it can, in fact, be found in many dictionaries, although it will often (incorrectly) be tagged as a “non-standard” variant of “all right”. It may have been that once, but no longer.
Then, you think nothing should ever be changed through common usage, and we should still write ‘‘And therfore, at the kynges court, my brother, Ech man for hymself, ther is noon oother.’’
And you hate, hate, hate the idea that new spellings have become accepted just because a certain number of people misspelled them? Or did English reach some magical point of “correctness”, after which no more evolution is allowed?
But A’ight is cool, right?