Need help

History of car it had a new head a couple of months ago

Also looking at service history it also had new water pump

Purchased car 12 weeks ago

Last week the coolant alarm came up on dash checked water level and it was fine

Top hose boiling hot bottom hose cold, to it to local mechanic and he took it apart checked water pump and thermostat all fine

Filled it back up with water and anti freeze problem still there so really not sure

Also don't know if this is linked but won't start on key on cold start takes ages and runs rough Untill warm then the temp gauge goes from 90 to 130 and back like a yoyo with the coolant alarm going

Can any one help please