Poweramp starts/resumes on its own or pauses in car

Poweramp can start to play when a headset is inserted - you can disable this feature via settings => Headset / Bluetooth => Resume On Wired Headset.
Also some applications and/or devices may broadcast Headset insertion event sometime (for example, FM radios or some headunits are known to do that) - disabling Resume On Wired Headset option will help in this case as well. 

For BT connection, there is a separate, Resume on Bluetooth option, which is disabled by default.

Please note, that if both options are disabled and Poweramp still resumes on connection, this means device ROM (or most probably - some other app), sends MEDIA_PLAY command, which is the same as headset PLAY button press. This is controlled by Respond To Buttons option.

Poweramp v3 shows all the recently processed commands and their sources in Settings / Headset/Bluetooth / Last Processed Commands.

Also, some car head units are known to send explicit MEDIA_PLAY command when Bluetooth connection establishes, which Poweramp have to execute even if it's already playing causing playback toggle back to pause. Poweramp v3 has some logic/code to ignore that.