FAA squadron codes early 1940

[Pieter H]

I am stuck trying to find the Fleet Air Arm squadron codes in april-May 1940.
I think there was on the one hand a systematic coding scheme of an carrier letter, squadron number and individual letter.
So HMS Ark Royal squadrons started with A, followed by the squadon order number. A2 was No. 810 Sqn, A4 was No. 820 Sqn (I think). These codes were then followed by the individual aircraft letter. A2A, A2B, etc.
Simlarly HMS Glorious (G), Furious (U), Hermes (H), Eagle (?) and Illustrious (L).
The list of codes I compiled (without any claims to correctness):
810 A2
820 A4
802 G6
812 G3
825 G5
816 U4
818 U3
814 H3
824 5
806 L6
815 L3
Still missing: 800, 801, 803, 804, 813, 819, 821, 823

So question 1: can someone confirm this was the coding scheme, and if yes what were the squadron codes?

But then there seemed to be a second coding scheme, essentially a number followed by the individual aircraft letter; 2Q, 4A, 4B, 5H, 6L, etc.
What confuses me is that these codes pop up all over the place, and at a certain moment they seem to have been used by multiple squadrons.

So question 2: was there any systemacy behind this second type of coding?

All in all pretty confusing, this FAA coding. Hope someone can bring clarity.

Regards, Pieter