As far as missing a flight goes due to being delayed, a hard cut off is no different to BA's hard cut offs at heathrow.

It is annoying when it happens, but what EK did at DXB is no different to how BA works in London

As far as vegetarian options - did you actually order a vegetarian meal?

That there were babies on a flight - well so what , that can happen on any airline

I am lost on why you needed to come back a day early due to getting there late however making the change coming back will require paying the appropriate fees

I would find it v surprising and unlikely that BA would refund a ticket due to a delayed flight causing a missed connection