4- What's the unit's Identification letter (A letter on a label on the box that indicates what version it has)?
(PSP 200x ONLY, Does NOT Apply on 100x or 300x)
Here's a picture of a label found on the PSP box that has the letter on it:

Note that this label is only present on an original style box (The small, normal box. Not like those large "Limited Edition" Boxes).
Anyway, See the G there?
PSP-2000 CW
100v
G
That G is the letter in question. Here's a list of all the letters that the 2000 series ship with and their Motherboards:
[b](No Letter) = TA-085v1
A = TA-088v1
C = TA-085v2
E = TA-085v2 or TA-088v1
F = TA-088v1 or TA-088v2
G = TA-088v1 or TA-088v2 or TA-088v3
J = TA-088v3
Some Labels have an extra code written on it, usually “ss259”. That doesn’t matter, just look for the Capital Letter next to it (to the right).
Note that the G PSP in the picture is my personal PSP. It came with a 3.95 Official Firmware (OFW) & I hacked it.
5- What's the Box's Serial Number?
(PSP 2001 ONLY, Does NOT Apply on 100x or 300x)
If your box doesn't have a label with a letter in it, like the G in the third method, then it should have a label with serial number.
Here's a picture given to me by one of our members:

If the serial number is less than AB021600000, then it has a TA-088v1 Motherboard.
If the serial number is more than AB022499999, then it has a TA-088v3 Motherboard.
This is related to the HU~ Serial Number (Method 4) & only applies on American Piano Black PSPs.
This does not apply to ANY other PSP; only the 2001 Piano Black edition. I currently do not have any similar information on other PSPs, especially Limit Edition PSPs.
6- What's the PSP's Date Code?
(PSP 200x ONLY, Does NOT Apply on 100x or 300x)
This is where you would find the date code:

Note that American 2000 series (2001 PSPs) & Japanese PSPs (Both 1000 series & 2000 series) Don’t have those date codes on them, just like the 2001 Piano Black PSP pictured above.
The Motherboard list for the date codes isn’t ready yet, so I’ll just mention the hackability.
The 2000 Series Date Codes go as follows:
7C: CHA.
7D: CHA.
7(Any later Letter): CHA.
8A: CHA.
8B: CHA.
8C: Has Very High Chance that it is PHA or NHA.
8D: PHA or NHA.
This information isn’t 100% valid. I’m still doing some research on it, & I will be updating it whenever I know anything new.