After parking car is in park and is rough idlex

Check clutch master and slave cylinder, and throwout bearing.

If automatic, change transmission fluid and go from there.

Vacuum leak, cracked hoses or gummy vacuum hoses.

idle air control is bad

Here are the common cause of surges, cold stalls, stalls at stops, slow idle speed, erratic idle speed, rough idle and engine hesitation (and other problems), it is in most cases the idle speed control air-bypass valve and or throttle valve and upper intake, these area's get full of gunk and combustion residue over the miles and cause idle issues (stalls, low idle) like yours.
To correct this problem I want you to get a can of intake cleaner (ABOUT $5.00) from any local auto parts store like NAPA or Carquest, do not use carburetor spray, intake cleaner only or u will damage the Teflon coating inside the throttle valve and air bypass valve, it is made by a company called CRC, remove the air intake hose to the engine, hold the idle high so the engine won't stall, then spray the can of cleaner into the intake while keeping the engine running, use at least 1/2 the can, shut down the engine and disconnect the battery for 5 minutes, then restart and complete a number of mixed driving cycles, town, freeway, stop and go etc., after a few days the problem will go away as the system will relearn to the clean intake.

I would try some concentrated injection cleaner look over tune up

The charging system is doing its job It seems to have an electrical short which is draining the batt. If u have the know how to ck & repair electrical shorts then go after it, if not, take it in.

check for vacuum leak. Has someone changed the pcv? If so they may have left off the o-ring seal off the bottom of it.

start by pulling hose off egr valve see if idles smoother almost instantly

there are 2 things that usually cause this, one is a dirty intake idle control valve and the other is hard engine mounts, I would say that both most likely apply to your car. try cleaning the intake with the following procedure from Ford.
Here is the most common cause of surges and stalls and low idle rough idle, it is the idle speed control air-bypass valve and throttle valve (IAC for short), they get full of gunk over the miles and cause idle issues (stalls, low idle) like yours, Get a can of intake cleaner from any local parts store, not carb spray, intake cleaner, it is made by a company called CRC, remove the air intake hose to the engine, hold the idle high so the engine won't stall, then spray the can of cleaner into the intake while keeping the engine running, use at least 1/2 the can, shut down the engine and disconnect the battery for 5 minutes, then restart and complete a number of mixed driving cycles, town, freeway, stop and go etc., after a few days the problem will go away as the system will relearn to the clean intake.

your probably feeling a rough idle of the engine. need a tune up?

in park the engine is not loaded down, just idling at a low rpm=rough
in drive with brake on you have put some load on motor also at low rpm=rough
in drive on the road engine is at higher rpm, = smoother

generally 4 cylinder motors idle a bit rough, especially if one spark plug is not firing right or fouled or one bad spark plug wire. tune up may fix it. if it is not stumbling real bad or stalling then you can live with it.