- How can we measure the distance of a path accurately while it's happening? Like an odometer. Less than 1% error.
You benchmark the current position against a previous position and then calculate/measure a distance between the two. Less than 1% is very easy when using an accurate measuring tool between to well marked positions. Using a 100' tape measure between two points 90' apart probably is well with in this accuracy. Typical GPS is not designed to do this type of measurments. Your use of 1% is relative to what is being measured. GPS is probably with in 1% accuracy when measuring the distance between a point in Dallas, TX. and a point in Denver CO.
- How can we measure the lean angle of a motorcycle with respect to gravity in degrees?
A mechanical gimbled gyroscope has been the standard for many years.
- How can we measure the line/track around a motorcycle race course during the race? 1-3ft acc would be nice.
Using a GPS satellite is not a realistic expectation. You will probably need to use benchmark and measurement tools at the track itself. Just remember the laws of physics generally ignore wishful thinking.