You were accommodated on the correct flights. Yes there was a problem over the seat. A connection was tight - but you must have known this when you booked the flight - and they ensured you made the transfer.

No web check-in for a child? Fine - if they don't want to offer that facility.

Holding them responsible because your child was worried that you might not make the flight is pushing a bit IMHO. I don't see how the airline can be responsible for the customs officer (I think you meant immigration officer) not knowing about the visa rules. Ditto passengers staring at you thinking you might be illegal... I doubt if they thought that anyway.

Yep the flight was delayed - you asked for lounge access because you were in business class, and then got it. There was some confusion about security when you left, but that was also fixed.

Yep nice if they had made a gesture and possibly in their commercial interests to do so, but they chose not to. I don't you're entitled to compensation and they did apologise after apparently making some effort to investigate. In fact it seems that when you weren't happy at the time some staff apologised. It seems unlikely that the check-in staff deliberately "tricked" you into thinking someone was there when he was away.

Thought it all amounted to an unhappy experience I think you should accept the apology. If you think you've been wronged at least you got some justice by reporting it here.