Thanks for all the insights. The garage told me those warnings are: Oil change and service warning, plus car key battery replacement. They also said they will replace the timing belt and water pump (how do I check this was done?).
I have got a feeling that independent car inspection is the only way forward so I know exactly the state of this car or other car and can make fact based decision. But if someone tells you after they already decided to advertise their car that
they still need to do service, MOT, replace water pump and timing belt, change oil, top up AC and replace fob battery.... I think it's correct to assume it's better to walk away