Karvonens formula can work very well if a known HRmax is used but what lets it down is that it still uses 220-age as a predictive equation to give a HRmax.

When I was working in health development, Karvonen formula was used with a modified 220-age predictive HRmax formula used. As it was working with patients with strokes/heart attacks/obese etc clients and knowing the formula has a +/- 15bpm varability, 205-age was used instead to factor that varability out of the equation. Working with these types of clients it will not affect them as it will performance athletes.

If looking at performance athletes and if HRmax data is not present, there should be no issue if getting a near max HRmax by doing a timed 2km run. By the end of the run they will be sprinting to the line giving you a HR very close to HRmax without having to complete a labortary testing. This would be a prefered method for capable athletes then decide what type of training to complete and how HR will influence training.

Yes that would work - it may not be a true HRmax but will be very close to it and will good enough to work from.

HR Reserve just needs a HRmax whether it is from max testing or predictive equation with it being more accurate with a true HRmax.