Rowan - We had the Disneyland one too! For 'Dis', we span on the spot; for 'ney', we touched our knees; for 'land', for some reason, we touched our back with one hand (usually right, if I recall) over one shoulder. We tried other verions too, but 'sea-sea-sea' and 'disneyland' were the most common. I believe we also had 'Diz-diz-diz' and 'knee-knee-knee', but I never did them all as verses of the same one.
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Azizi - 'A-B-C-Together' is now incorporated by my sister's generation, I'm informed, into a long clapping game containing about 5 different ones - sadly, she couldn't say which. It's almost a list of instructions. It seemed almost half-forgotten - most people would peter out near the end...

Put your hands together, fingers pointing at the person opposite.
A (slap backs of left hands together, own palms still joined)
B (same with the back of right hands)
C (A but stay together, rather than slapping past)
Together (each clap right hand against own left hand)
Up (Right hands clap above the 'together' hands)
Together (bring back together)
Down (Right hands clap below the 'together' hands)
Together (bring back together)
(Then it gets tricky. The version I learnt went:)
Bow (stop holding any hands together and bow forwards from the waist - you may bump heads, though you're not supposed to)
Front (Un-bow)
Turn (turn around)
Together (bring hands back together, and clap right against left - this was sometimes missed)
Spin/Sing(some people would spin; some found this too similar to 'turn', and would think it referred to the end part)
Together (bring hands back together, and clap right against left - this was sometimes missed)
Yo! (hands up triumphantly, if you felt like it)

But there were variations I saw including shaking hands, the line "turn around, touch the ground", more clapping going "1,2,3" - none of this is very herlpful, I know. As I said, it seemed half-remembered, and was embelished.
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As for games 'choosing it', I believe the Mickey Mouse one (mentioned earlier) went (in our various accents):

Mickey Mouse/Moose
In his house/hoose
Pulling up/on his trousers/troosers
[possibly another line]
What colour will they be?
[person landed on]-Blue[or other colour]
B-L-U-E spells blue
O-U-T
O-U-T
O-U-T spells out!

This isn't quite right - I'm going to ask a few old friends about both this and the ending of 'Kings and Queens arrivin', just to clarify. It did involve each person putting out both fists (including the person saying the rhyme), and each FIST was counted, and both fists had to be 'out' before the person was 'out'. Last man standing, so to speak, was 'It'.

The 'fist' thing was used in this one too:

Ingle angle
Silver bangle
Ingle angle
A
B
C
D
etc

If you had the letter in your name, that fist was out. I remember that one very clearly - with three middle names and a double barrelled last name, my name contained most of the alphabet, so I hated that one. But it was used often, because people couldn't 'count ahead' to work out who would become 'It'.

And Azizi - it's wonderful to find someone else interested too! ^_^

-Viracocha