Electronic – Parasitic Capacitor current of an inductor

The basic reason for using a parallel tuned circuit as the exciter is one of efficiency. If your inductor and tuned capacitor are 33uH and 75nF, resonant frequency will be about 101kHz. If you do the math you'll see that a lossless tuned circuit like this exhibits infinite impedance but still circulates high current between cap and inductor.

Lossless circuit are of course impossible but making the losses as low as possible means that if your inductance is 33uH and your applied voltage is (say) 40VRMS at 100kHz, the current in the inductor is: -

\$\dfrac{40V}{2\cdot\pi\cdot F\cdot L}\$ = 1.93 Amps

Your H bridge won't even be breaking into a sweat because it won't be supplying anything like this current. This current is due to the voltage across the inductor but the capacitor has the effect of performing "power-factor" correction and because the losses are low maybe the H bridge will be supplying in the order of 50mA to a couple of hundred mA.

However, your H bridge is exciting the coil/cap with a square wave and there will be losses due to the harmonics within the square wave. Because of this it makes sense to feed the coil/cap via an inductor too - somewhat smaller than the coil (maybe 1 quarter). You will also need to retune the capacitance to compensate for this. Some experimentation in this is required to get best results but, you should aim to reduce the H bridge's current to avoid it overheating.

I'd also say make one larger coil suitable for all three inductive loads. The larger coil can be any regular shape that suits your requirements for placement of the receiving coils.

Optimum performance is when the receiving coils are also tuned with a capacitor but, because the induced voltage is in series with a receive coil, the tuned circuit behaves like a series tuned circuit and, if the coupling is too great it will heavily detune the transmit coil when it is close by. You should aim for a minimum gap or incorporate circuits in the H bridge that current limit.

I strongly advise you to use something like LTSpice for simulating this - you'll learn a lot about the various interactions. I'd also recommend you read a bit about tesla coils because that is what are are intending to build (when tuned as per my thoughts).

1/2) More or less, I try to clarify, It seems to me you believe your graph in figure (2) shows R and L variations w.r.t frequency.
That graph simply shows impedance of a parallel resonant circuit made of approx constant 100nH inductor, 45kohm resistor and a \$\frac{1}{(2\pi\times 2\,\text{GHz})^2\times 100\,\text{nH}}\approx 65\,\text{fF}\$ capacitor.
This is one first level approximation which may however be good in many circumstances.
Then one can argue resistance is frequency dependant and add this to the model, the same for inductance and capacitance but this can usually hardly be seen on graphs unless you carefully measure, analize and fit curves to models.They are ususally hidden in measurements errors.
Then you can add many other extra parasitics and non linerities outlined above by other contributors, but there's no such an evidence in the sweep you posted.

b) Your meter shows variable (possibly negative) inductance just becouse you ask it to do so. It just measures an impedance, one complex ratio between voltage and current and then represent it as you configured it to do: you asked for Ls+Rs and if measured impedance phase does not agree with that model it just keep computing and findes "negative inductances".

Usabilty boundary (green/blue transition in fig. (2)) is not function of your component parasitic only, but it depends pretty much on the rest of the circuit e.g. if using that inductor in a resonator you should add stray capacitance to the computations and see if you get consisten numbers.

4) Yes SRF is that blue to red boundary.

3) Dimension do count. For resistors and capacitors usually the longer the part the higher the stray inductance. E.g. small SMD 0204 or 0603 may exhibit a few hundred pH while some big HV MKM capacitors I happened to use were specified as 7nH/cm w.r.t to terminals pitch.