We would capitalize both Roman and Venetian in those uses: Roman shade, Venetian blind.

Yes, if the organization's formal title for the person is chief executive, it would be capitalized when used immediately before the name: Chief Executive Joe Blow. Lowercase it after the name: Joe Blow, chief executive of Company X. The titles entry gives more detail.

It's $1.2 billion to $3 billion or between $1.2 billion and $3 billion.

The dictionary that we use, Webster's New World College Dictionary, defines a century as any period of 100 years. 

Yes, that's correct.

I would say: The store is bigger than it looks from the street. As your question indicates, people's interpretations of these terms are sure to vary. So you're better off rephrasing to avoid ambiguity or confusion. 

Thank you for noting that. We will make the correction to Naval Station Norfolk today in the online edition, and put it on the list for the 2018 print book changes.

The AP social media guidelines chapter of the Stylebook offers extensive guidance. It includes: 

Never simply lift quotes, photos or video from social networking sites and attribute them to the name on the profile or feed you found them under. Most social media sites offer a way to send a message to a user. Use this to establish direct contact, over email or phone, so you can explain what you're working on and get more detailed information about the source.

Also from that section:

If you come across photos, videos or other content that you would like to use in your news report, you'll need to verify the authenticity of the piece of content. You'll also need to determine who controls the copyright of the material and get permission from that person/organization to use it.

See the full chapter for many more details.

We would spell it out on first reference. 

It would be cyberscam, per the cyber-, cyberspace, cyber entry: Follow the general rule for prefixes and do not use a hyphen: cyberattack, cyberbullying, cybercafe, cybersecurity.

We don't have a style for an abbreviation for data communications (our style would be no abbreviation at all).  The fact that you found so much inconsistency in your search indicates that the question is, indeed, unsettled throughout the industry and there is no single correct answer. If it helps, a few similar examples from elsewhere in AP style: We use dashcam as shorthand for dashboard camera, and bodycam in some situations for body camera. Thus, datacom (no capital letters) might be a good choice if that makes sense for your audience(s). Consider what is likely to look right to your biggest audiences. Then be consistent in using what you choose.

I'd go with O.K. Corral, in keeping with our guidance to use periods in most two-letter abbreviations (in this case, an abbreviation for Old Kindersley). This is not to be confused with our style to use OK (no periods) rather than okay.

Our general style says: Use periods in most two-letter abbreviations. Use all caps, but no periods, in longer abbreviations when the individual letters are pronounced: ABC, CIA, FBI. 

We also say: The preferred form is to avoid an abbreviation and use instead a phrase such as: John Jones, who has a doctorate in psychology. ... Use such abbreviations as B.A., M.A., LL.D. and Ph.D. only when the need to identify many individuals by degree on first reference would make the preferred form cumbersome.

Since we try to avoid abbreviations, we don’t have a specific style on most of the examples you list. But the guidelines above can serve as a general rule of thumb for your needs.

AP style uses Latino or Hispanic for general references to people from, or whose ancestors were from, a Spanish-speaking land or culture or from Latin America.

Yes, it's paid.

We don't have specific rules or guidance on paragraph length. In general, though, our guidance is to keep the reader in mind. Make readability one of your top goals. Thus, breaking the paragraph into separate items in a dashed or bulleted list likely is your better option. 

A few guidelines on lists: 

It would be bankwide without a hyphen using guidance in the -wide entry.

We don't have a style specific to user interfaces or experiences, so you may want to consult more UX-specific sources and authorities. The question seems to be debated online a fair amount.

AP style is multistakeholder, multiperformance (though it might be better to rephrase). The multi- entry: The rules in prefixes apply, but in general, no hyphen. Some examples: multicolored | multimillion multilateral | multimillionaire

From the prefixes entry: Generally do not hyphenate when using a prefix with a word starting with a consonant.

Three rules are constant:

–Except for cooperate and coordinate, use a hyphen if the prefix ends in a vowel and the word that follows begins with the same vowel.

–Use a hyphen if the word that follows is capitalized.

–Use a hyphen to join doubled prefixes: sub-subparagraph.

As you note, U.S. readers (and quite possibly readers everywhere) could be confused by the term governates, whereas provinces is commonly understood. Thus our style, endorsed by our experts in both the Mideast and Washington, is provinces in all such uses. 

We also have a specific chairman, chairwoman entry that gives the answer: Capitalize as a formal title before a name: company Chairman Henry Ford, committee Chairwoman Margaret Chase Smith. Do not capitalize as a casual, temporary position: meeting chairman Robert Jones. Use chairperson, chair or co-chair if preferred by an organization.

In the next edition, we'll include a chairman/chairwoman example in the titles entry. Thanks for asking.

Yes, our style for board of directors is lowercase in all uses, including when combined with a corporate name.

He went 7-of-10 passing (as a modifier). He ended the night 7 of 10 (assuming the context is clear). 

It would be "an estimated $14 in return for every $1 spent." But if no figure is used for the latter amount, it would be "an estimated $14 in return for every dollar spent." See the dollars entry in the Stylebook.