2000 mustang gt bogs down while cruising and randomly from a stop

Did this start suddenly, or over a period of time? What CEL’s have/are being thrown? Find access to a decent Scantool, see pending Codes, view the Sensors @ operating Temp, Motor at Idle- look for any which are not making real-time corrections. Datalog with the Scan-tool so you can observe Sensors after a Drive Cycle, I’d first look at:
1) Dirty/Bad/TPS. May have dead spots between Idle and WOT. A Potentiometer (like turning an old, worn out rotary Volume Dial, speaker “crackles”) it provides variable output to the ECU coinciding with TB Butterfly(ies) position. If dirty, worn- (like the Radio example) irregular output to CPU occurs, poor/or no Throttle response from affected area(s) result.
2) Bad 02 Sensor/Wiring. The O2's provide feedback to the ECU to manage/ensure fuel/air ratio is not too rich, nor lean under normal conditions (closed Loop). However, at WOT the CPU defaults to open Loop, & fuel/air mixture is then determined by the fuel Map.
3) Dirty/Bad MAF. Working with MAF/O2 Sensors, Provides CPU with information, CPU modifies Fuel Injector Pulses to provide Correct A/F Ratio (14.7:1).
4) Vacuum Leaks in Intake or lines. Any Vacuum leakage may decrease throttle response. Leakage of a Cool Air or OEM Intake, between the MAF & TB, especially- will cause significant issues regarding smooth, linear ‘off Idle’ acceleration, Performance.

There are many things that may cause this issue, usually simple. Car functions correctly @ WOT, open Loop. Seems like a Sensor issue, Wiring to Sensors, or Vacuum leak, from provided Info. . CPU Codes are very important to post if you can, with any additional(s), E.G; Car’s Build, recent work done, any other issues, more specific Driving Data in different conditions, etc..
Cheers!
 
+1 on above.

At the risk of sounding like a broken record. Start with the basic tune up including the battery and charging system. Pay special attention to the ignition system. Is there any moisture in the spark plug wells? What is the condition of the COP boot insulators? A full set of (8) COP boot insulators is less than the cost of a single new COP.

How about the spark plugs themselves?

When the charging system and ignition system is in tip top shape then move onto more difficult items like excessive EGR flow.


Howto perform charging system voltage drop test
https://www.stangnet.com/mustang-fo...perform-charging-system-voltage-drop-test.56/