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The stalling could be an airleak after the airflow meter, any air dragged in here isn't 'seen' by the ECU and so not compensated for and can lean the engine out and can also allow the engine to rev up when not desired causing rough running.
As its a mechanical fault it tends not to turn on the fault light and you can sometimes hear a 'hissing' noise with the engine running.
Check the hose clips for tightness and inspect the trunking for any cracks or splits and also all the vacuum system, the small bore pipes and fittings for cracks and missing parts.
The best way to locate a leak is to have the engine running and warm and then spray lighter gas /propane around each joint in turn. If the engine rev's up you've found your leak.
Work your way through each possible joint one at a time and you should find it. I use a slightly flattened piece of brake pipe and some rubber hose from the can of lighter gas to provide a spraying 'wand' and allow a direct blast of gas into each area, especially those difficult to reach with large implements.
It’s also worth getting the fuel pressure checked as if this is low due to a blocked filter or faulty regulator or even a poorly pump will all result in insufficient fuel being delivered to the engine
Might also be worth cleaning out the idle speed control motor / valve as these get clogged up with carbon and some brake cleaner washed through helps free things off.
Might also be worth checking the wiring and connector to the airflow meter for any signs of corrosion or damage. you can do a quick fault find if you unplug the meter and run the engine without it.
if the engine condition is the same then chances are the meter or the connection to it is faulty
Air leaks are very temperature dependent as gaps can open or close up as things expand with heat, so the weather and engine temperature can effect them.
This leads them to be quite intermittent in the case of mild leaks
its also worth cleaning the airflow meter by removing it from the car and spraying the exposed sensor wires inside the tube with a brake or switch cleaner - ensure that the cleaner is one of the old fashioned, non Eco type that does not leave a residue
On no account touch the sensor wires with anything physical as they are extremely fragile
as for the steering feeling sloppy they aren't the tightest even when in good condition but
check for worn suspension joints - jack the car up so the wheel is off the ground (you’ll need to do this for all 4 corners) and shake the tyre from top to bottom and from side to side (with someone holding the steering wheel on the front) there should be no play in either direction. Any play in 1 direction will usually require a joint to be replaced, if there’s play in both directions then the wheel bearing may be at fault. If theres play only up and down its the strut top mount - to find this one you have to shake the suspension strut it self up and down with the wheel off the ground - so you may need to remove the wheel to check this one.
Now with the car jacked up on that side with the wheel about 2 inches off the ground use a steel bar under the wheel and lever the wheel up and down slightly, you should be able to look at the end of the axle and see if the suspension arm is moving up and down separately to the axle.If so replace the bush