Planning to do:

SIN-PEK-ICN (inbound on SQ, outbound on OZ)
KIX-CAN-SGN (all with China Southern)
CCU-BKK-CTU (all with Thai)

So am I right in saying I do not any visas for this itiniary, as those 3 cities are all 72hrs visa free for my country (UK)?

I have been visa free before in Beijing, and there was a little complication as the guy kept asking me at immigration, "show me your friend who is picking you up" and I kept saying "I don't have a friend picking me up! I AM USING A TAXI to go to a hotel!". I didn't understand why he was asking that irrelevant question but in the end it got sorted (this was late night in PEK T2 on a flight from Seoul).

I do not need to apply for anything beforehand do I? I just have proof of my outbound flight and proof of my hotel address.