They all want to look at something a little different. Yes, for balancing it especially. Then at EGT to see if they dropped any cylinders. One team looks at steering input and yaw rate to monitor the driver's input. We mount the G meter along the direction of travel.
Any shake usually shows up in drive shaft speed.
Yes, by looking at the shape of the drive shaft curve and comparing it to historical runs. Our RPMs are good to about 1 part in 65000. Depends on application. Everything but top fuel wants to go in the center of the pipe about an inch from the flange. Depends on the class of car.