AM/PM vs a.m./p.m. vs am/pm

I used to think PM/AM was correct, but at some point, I switched to using p.m./a.m. for reasons I can't recall. I know that in practical, casual writing, people tend to use whatever form is most convenient to them, but I'm curious about what the official usage—should it exist—actually is.

What is the correct or official form for these initialisms?

1. Are they capitalized?
   • 4 pm
   • 4pm
2. Is there a space before them?
   • 4 PM
   • 4PM
3. If the correct usage is a.m./p.m., how does this affect punctuation at the end of a sentence?
   • Should we meet at 4 p.m.?
   • Let's meet at 4 p.m..

(Let me know if these should be split up into individual questions, but I figured that because they were all related to these initialisms in particular, it might be okay to ask them all in one question.)

Solution 1:

Because the initials in question are of Latin origin ("post meridian"/"ante meridian"), it makes sense to keep consistent with other Latin abbreviations, e.g. (oh there's one right there) "i.e.", "e.g." when there are two words.

I would say, use whatever seems natural, but I prefer "10 p.m." and "8:30 a.m.", for example.

Solution 2:

An alternative from The Guardian Style Guide:

times

1am, 6.30pm, etc; 10 o'clock last night but 10pm yesterday; half past two, a quarter to three, 10 to 11, etc; for 24-hour clock, 00.47, 23.59; noon, midnight, not 12 noon, 12 midnight;

Solution 3:

Instead of AM and PM (in small caps), p.m. and a.m. -- with lowercase and periods -- are the preferred way to indicate time of day.

According to the The Chicago Manual Style used by journalists.

Solution 4:

If you leave out the dots, you should also omit the space, otherwise am looks like an independent word. Personally, I prefer to include both the dots and the space.

In the USA, I've seen them reduced further, with times like 8:00a and 6:00p. Worse, this was on a timetable (aeroplanes), where I'd expect to see the 24-hour clock used. It confused me for a while. I can't imagine how confusing it must have been for travellers from countries where the 24-hour clock is used everywhere.