Lot of questions... here a a few answers to ponder.
Poor running could be a result of so many things it's hard to say if a carb sync would help. Some things to look for are bad gas, clogged air filter, dirty carbs, improper float levels, among others.
Under the tank there'll be 2 vent hoses, possibly an electrical connection for the fuel gauge (don't know which generation you have), the fuel line to the petcock and a vacuum line to the petcock... all of those need to be disconnected and the tank completely removed from the bike.
You'll need to plug the vacuum line that attached to the petcock and hook an alternate fuel source to the fuel line (spare gas can, etc.) You'll need a fan in front of the motor to provide cooling while the engine gets to temp and during the sync procedure.
You'll benefit from installing some carb sync extension to the carburetors - it's much easier than trying to connect the MotionPro tool directly to the carbs. A good example is shown in the Jet Kit Installation Guide found in our downloads section. The extensions only have to be added to carbs 1 thru 3 since the 4th carb (right side as sitting on the bike) is easy to access.
I personally like to warm the motor prior to hooking up the carb sync tool to avoid sucking mercury back into the carbs caused by too high of RPM's. Once the motor is warm, the tool is hooked up and the fan is running it's time to make the adjustments. Get the motor up to 1,700 RPM by using the idle adjust screw or throttle lock. Between each pair of carbs (1 & 2 / 2 & 3 / 3 & 4) you will find a screw that's accessible by looking straight down from overhead. These are the adjuster screws and they're very sensitive. Do not push the tip of the screwdriver into the screw head - use very light pressure or else you'll make things worse and not have an accurate reading.
You'll see the 4 columns of mercury will be likely at various heights while the motor is running - the actual amount of vacuum is not important... you are trying to balance so all four columns are equal in height regardless of where they fall on the scale. Start by turning the screw between carbs 1 & 2 - you will see how the 1 & 2 columns will get closer or further apart on the gauge... make them as equal as possible.
Next, do the same thing with the screw between carbs 3 & 4 - get those two columns as equal as possible. Do not worry about 1 & 2 during this adjustment. Now that 1 & 2 are close and 3 & 4 are close you can use the middle screw (between carbs 2 & 3 to balance each PAIR of carbs. Sounds more complicated than it really is.
You may need to repeat this a couple times - balance 1 & 2, then 3 & 4 followed by balancing those pairs to each other.
When all four mercury columns are at the same height your carbs are then synced.
Reassemble the gas tank and don't forget to remove the plug from the petcock vacuum line. Make sure all hoses are connected properly and not kinked in any way. Hope this helps.