Yes, just that shape -- but if you want a lower operating frequency, try for >50 turns, probably using even thinner wire.
A coin will increase the magnetic coupling between the 2 coils not reduce it. This is because air has very low magnetic couoling. Most metals/alloys have bettwen than air megnetic coupling.
No, it will block. Very few coins are ferromagnetic at these frequencies, and probably none that are the size and value OP is looking for. Those are usually a bronze or cupronickel alloy, silvery or golden in color, nonmagnetic, and reasonably conductive (thus, blocking AC fields effectively).
Even at low frequencies (10s of kHz perhaps), I doubt most magnetic coins* would increase transmission. They're simply too large, and eddy currents (especially from the plating) will block more than transmit. You're also blocking the field anyway, if the arrangement is two coils, smaller than a plate, on either side of it; this is true even if the plate is ferrite. (But many arrangements can be contrived which result in more or less field, depending on material. For example, coils that are on equal centers but rotated perpendicular, against a diagonal plate.)
*That I'm aware of: some very rare US cents (1943ish); most countries' smallest denomination, cents or nickels (usually copper plated for corrosion resistance and appearance); and moderate age Canadian coins (5-25c pieces were high nickel). I haven't looked at an exhaustive list in a long time, so look it up to be sure!
It occurs to me, if you need great sensitivity, and many degrees of freedom, to identify not just coin presence, but size and material as well: you could set up a two port network analyzer, basically, and measure reflected and transmitted power and phase. Phase will vary with resistivity and permeability (skin depth) and thickness. Even better if it's done over a wide frequency range, so the material thickness becomes apparent (skin effect is only an exponential cutoff in an infinite solid; in finite materials, waves echo back and forth, forming weak standing waves).
Tim