For 30ghz, there likely are no commonly used active filter topologies. However you can use galium arsenide FETs in this region to build various circuits (PA, LNA, mixer, VCO, etc), never seen them used at 30ghz but have seen them used for 24 Ghz I would think you could extend their operation to 30Ghz if care was taken.
Passive filters will definitely be implemented with microstrip structures, lumped elements will not be useful at these frequencies. You'll also need to find a very good substrate to work at 30Ghz.
Falloff is dependent on the topology you use and the number of poles in the filter much as it would be at lower frequencies. For instance Chebyshev filters are common.
My only experience near such frequencies was a 24Ghz FMCW radar front end, that used GaAs FETS for the PA, VCO, mixer, a hairpin bandpass filter and was built on Roger 5870 substrate. I didn't do the RF design this was an externally sourced design and we ended up using a 10.5Ghz variant of it.
My initial thought is that your desired bandwidth is really wide, and that will greatly complicate the design.
Your best bet is to get a couple books on RF filter design, make sure your up on your calculus and start running some simulations using various topologies. Ansoft Designer and Microwave Office are the two simulation packages that i've bumped into in the past for RF circuit simulation. I believe they both have free trials.
Driven shield
It is possible to use shielded wires between the electrodes and the pre-amp without a lot of influence from the shield's added parasitic capacitance (your 2nd dot). The signal itself won't be hurt much because it is very small compared to the common-mode component. To understand this, imagine a tiny differential signal on top of a much, much larger common-mode signal (mostly caused by 50 Hz or 60 Hz mains voltage) and a DC-to-low-frequency component caused by the interaction of the tissue with the electrodes and the body itself. As far as I understand the issue, the interference coupled onto the signal via the cable's capacitance is much worse than having the signal itself fed through the cable capacity.
The trick is to actively drive the cable's shield with the common-mode part of the signal instead of connecting the shield to the pre-amp's ground. Some years ago, I've built such pre-amp with an active guard and was able to use shielded wires as long as 2 m between the electrodes and the first stage of the amp. The schematics can be found in this thesis (not mine, but conveniently includes the most interesting schematics of my EMG amp). Please see fig. 8.7, 8.8 and 8.9 and all the stuff around them in chapter 8. Fig. 8.12 discusses how interference is capacitively coupled onto the signal of interest. Sorry, the thesis is in German, but I hope the images and schematics are international.
A good place to pick up the common mode signal is the "middle" of the gain setting resistor of the initial InAmp (again, see the thesis linked above).
Driven right leg
The right leg is used as a reference to measure signal on left leg, left arm and right arm.
The concept of a driven shield can be extended to actively drive the patient, and the connection is made at the location used as a reference for the signals to be measunred, which is the right leg. This is known as a driven right leg (DRL); there's a good discussion about DRL amps in this article by EDN.
If your measurements are not taken from a human body but from some cells in a dish, you can probably put the DRL electrode onto the bottom or into the jelly / growth medium, close to where your reference electrode sits. This way, you use the same strategy as you would in the sense of a DRL setup.
Notch filter
Also, If the hum is really bad, you can put a notch filter at 50 Hz or 60 Hz into the signal path, but this will also hurt the signal of interest.
Very important safety note: The electrodes must not have any direct galvanic connection to protective earth (PE). This is necessary because once the patient gets connected to a potentially lethal voltage by a fault in another device around the lab, the fault current will have a very good path through the patient and via the electrodes to ground. When talking about a ground reference around the electrodes or the pre-amp, be sure to make this a ground referenced to the pre-amp only and not to the real ground usually known as PE! This usually requires an isolation amp somewhere around or just past the pre-amp, or a digital isolator if you wish to have the ADC close to the pre-amp. More about this in DIN EN 60601-1 and other relevant standards.
Best Answer
I'd recommend A) use a battery, and B) before you put the electrodes across your eyes, place them someplace with less potential for damage, like your arm. If it hurts on your arm, don't continue.
Use disposable pediatric ECG electrodes, if you can get them.
The safest course of action is to isolate the output before hooking it up to an oscilloscope, using something like an Avago HCNR200 (cheap, requires support circuitry) or an isolation amplifier (expensive, but easy), but if it doesn't hurt on your arm, you should be OK.
UPDATE: Also, don't place the electrodes on somebody w/ implanted electronic devices. Probably won't do anything, even worst case, but better to avoid the expensive risk of destroying a device.