Problems with my gf 05 mazda3. Help

[cosic]

2005 Mazda3 150,000kms
Automatic

My girlfriends car has a list of unknown problems. Before we take it into a dealership or mechanic, I wanted to see what you guys think about it.
-Car doesn't turn on in park. I have to put it on accessory, switch to neutral, and then the car will turn on.
-Very loud and pulsing idle.
-getting 10kms/liter
-Engine randomly shuts off while at red lights.
-Car won't turn on right away after filling tank of gas

[peterm15]

Any CEL's

[Reddie1337]

The park issue is a safety neutral issue, maybe the cable isn't adjusted properly anymore. Does the P light up in the cluster?

Very loud/pulse, could be a tune up, just not running right anymore.

10km/litre, also makes me think tune up and air filter check.

Stalling, also could be tune up.

And like Peter asked, any engine light?

These would be my first idea if there is no engine lights, but problems like that, normally set off engine lights.

[cosic]

Sorry guys, when I posted that I hadn't got a chance to drive it and see.

So after driving it. She's idling at like 750rpms. Within a short drive, it cut out twice while waiting at red lights.
There is a CEL.
Also, there's almost no difference from neutral to drive. I noticed this because I tried to avoid it stalling at red lights, so I'd put it in neutral to rev up the engine a bit, but i'd literally have to hold/force it up into neutral. If I let go, it would drop back down to Drive.

Thanks for your help so far, guys.