04 plate with 44k? That is low mileage!
Whining im guessing is where its not been used that much over the years so you may find if you use the car more the whining will disappear. Possibles are wheel bearings, driveshafts, gearbox etc.
As for the other issue; it probably needs a few good runs to clear the crap buildup in the engine. Again im guessing this car was probably used for round the town journeys etc. Maybe it didnt even hit 60mph before you had it 😃
Give the car a good service/oil change and do some motorway miles and that will help.
OH and welcome to the site :thumbup: