A look at baro graph shows you have prop wash hitting the sensor. Its fluctuating at all times within a range of 0.5 to 1.5 meters rapidly which explains pulsating motors. Another evidence is that during the beginning of your flight, you are sitting at off 0 alt before take off, however as soon as your props spin up, alt drops to -4meters, then you begin flying at 1-2meters alt, however again while landing it drops to -4m right before landing and comes back to 0 when copter is landed and motors are not spinning. Thats a clear sign of baro getting disturbed due to the air that comes back from the floor.
This is how your baro graph looks,However
TBS Discovery clone with APM
this is how it should look
TBS Discovery clone with APM
It seems logging for everything isnt enabled, so cant figure out if magnetic interference is present. However your yaw is very erratic(image below) even when the input is unchanged(red line) which usually points out to mag interference.
TBS Discovery clone with APM
Couple of other things which need attention are:
Power to FC is fluctuating a lot, crossing minimum threshold of .15v at times. I would never trust the power module that comes with APM. Its better to use a separate bec or ubec. Use PM only to check battery voltage and current consumption .
PID's are not upto the mark, if you observe roll vs desired roll, and similarly pitch. Most of the times your copter is overshooting while correcting after you request a change. But baro could be the culprit too.
TBS Discovery clone with APM
Suggestion:
Take a look at baro as most of your flight woes seem related to it because, a sensitive baro would never let you get optimum PID. And you cant auto tune without althold.
Dont cover the ABC lights on the board while covering baro, as light may get reflected to baro if you are using white foam specifically. Use dark coloured material. Just check the log of your 9" prop and see how baro readings look like & compare. We can move ahead to other issues once this is sorted, Infact you would only need an auto tune & everything should almost fall in place.