mrs just bought a mini cooper convertible 54 plate and i am a complete noob with them as i drive a calibra however i have two questions i hope you can help me with

just noticed that the hydrolic engine mount has started leaking is this an expensive fix?

and

when she pulls away there is a single beep its not the temperature warning and also there is no warning lights on the dash any ideas as what this could be as it is quite irritating