Will these PS3 downgrade
 

I own a PS3 slim Cech-2503A and a
PS3 Fat-CECHH

will they downgrade succesfully

Yes. my 320 slim is 2503B and is down gradable to 3.40 (use minvercheck to find out your minimum fw allowed) HERE, and Fats all downgrade to 2.xx and below, your HH should go to 1.97.

http://www.ps3devwiki.com/wiki/SKU_Models

You will however need a hardware flasher (such as Progskeet or E3) and a downgrade dongle.

is it also true that the FAT is the first which includes NOR flash

Correct.
As for the 2503, you can't know until you use Minverchk as mentioned above. If it tells you 3.55 or lower minimum version, then you can downgrade.

http://www.ps3devwiki.com/wiki/SKU_Models the info is right there.

CECHG and below = NAND

CECHH and up = NOR

ALL slims = NOR

@pereb27 yeah I never got the 25xx then 251x then 25xx release pattern on the devwiki, i guess its all about the date codes.... - best to double check with minvercheck

i know i can run CFW on the slim cos i ran it before.. apart from buying e3 flasher limited and the downgrade dongle do i need anything else

1x tin of elbow grease.

:P

Just kidding, you are all set.

Use minvercheck on your Phatty console, and report back :)

The last 2 numbers are region code, I believe they listed 251x (2511 and 2512 to be exact) because they were released on these regions (mexico and hong kong respectively) later than on the other regions but they're essentially the same.