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A Helmholtz coil is typically used to produce a uniform magnetic field. You could print two coils on either side of your PCB and use a via to connect them. The magnetic field will be stronger the smaller the coil, so probably design it as small as possible while still be acceptably homogenous in your 10 mm diameter region.


A connector usually has to introduce some mismatch; in fact the edge launches (the 'official' name for your connector) was designed to minimize that. In practice I agree with you, the line is short and you wouldn't have issues. Since the connector is more or less a solid piece of brass I'd suggest to properly ground the lower pins and use the upper ones ...

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