Induction heating follows the coil. Where the coupling gap is wider the surface runs cooler, where it narrows it runs hotter, and on anything other than a plain cylinder that difference is what decides whether case depth holds around the full profile. Getting it right is a matter of shaping the coil to the part rather than compromising the part to a coil that already exists.
On gear teeth, splines and internal bores, the field needs steering rather than simply applying. Flux concentrators pull the field into the region that has to harden and keep it out of regions that must not, which is what makes single-tooth and contour hardening practical on geometries a plain encircling coil would heat indiscriminately.
Coils are brazed from material of your choice to the profile the work requires. If you run your own induction equipment and need a coil built or replaced, send the part drawing and the machine details and we will quote against them.

Yes. Send the component drawing along with your machine make, frequency and power rating, and the coil is designed against those.
It depends on the profile and on whether concentrators are needed. Send the drawing and we will give a lead time with the quote.
Usually. A worn coil plus the part it was built for is generally enough to work from.