If products of combustion were detected to be escaping the casing of the boiler then ID.
Easy to assume the worst with the reputation that goes along with your chosen company.
It's near impossible to diagnose the circulation issue precisely without being at the property.
There's an air release valve to bleed air from heat exchanger which may of not been used when refilling the system, which could be a contributing factor in the issue but definitely not the cause of the signs of heat stress and leaking present on heat exchanger.
Pipe shouldn't of been cut for what can be seen in pictures alone, as at face value it appears to be classed as "At Risk" which would still justify advice of turning off and not to use, but not physical disconnection of the gas supply.
Ultimately though the heat exchanger issue should definitely be attended to first. The heat exchanger is showing signs of excessive heat with the ribbing being quite apparent.
I'd get priced up (from a different company preferably) for heat exchanger renewal (along with burner seals etc) and request a water quality test to determine if a flush is also required.
Once you've got that information you need I'd then still consider the option of replacing the boiler purely from a financial perspective due to potential warranty benefits of changing it out for new.
If it were in my house id change the boiler but can understand why it is more suited to others to replace only the heat exchanger etc.