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Axle-crown length is the length between the axle and the top of the fork crown, increasing or decreasing it pivots the bike about the rear axle and affects your headtube angle (amongst other things), increasing it decreases the head angle and vice versa.
As I said, a few mill either way won't make much difference. If you buy another "track" fork, it is likely to be a similar length/rake so won't change the handling. I'd just get another fork and fit a brake on it to get you going.
Edavies94
oheyitsd
Yes diameter of the steerer, most probably either 1 inch or 1 1/8, steerer length ofc and whether it's a threaded or a threadless steerer. You mostly want to match the axle to crown length of the old fork, you could probably adjust it 5mm either way without it having any noticeable affect on the steering.
You could just take the old fork to a bike shop to drill it for you, or do it yourself but you'll need a powerful drill and some good quality bits to get through a fork crown.