Rough running and prop surging
For the rough running check the primer seals, if they have a slight leak it will bleed extra fuel into whichever cyl has the primer line (#1?) Causing it to run rich. This would also explain the fuel running out of the plug hole after it pools on shut down.
For the prop surging - if you have an MT govenor check the serial number - early ones had a surging problem which MT should fix. Otherwise the prop internal fine pitch stop may be set wrong. This is not uncommon on new props. You can check this by winding the govenor fine pitch stop right out and doing a full power run to check the max rpm. Be carefull you do not overspeed the engine! On hartzel the fine stop can be adjusted on wing. On MT it will need to go back to the prop shop.