I presume these are pitch-only Theremins..
1.) You will need to detune the Theremins from each other, to frequencies which no not interact.
2a.) The length of the antennas is critical for tuning - a longer antenna has higher capacitance which results in lower pitch oscillator frequency - the reference oscillator must be correctly tuned to match the pitch oscillator frequency.
2b.) Increasing antenna capacitance also impacts on sensitivity in many ways - large 'background' capacitance with respect to player capacitance reduces sensitivity.
3.)Any shape antenna is possible provided the above issues are taken into account.
4.)the wire connecting to the antenna 'object' IS part of the antenna, making connecting wires 'insensitive' is not simple.. screening the wire adds huge capacitance to the total antenna.
5.) It IS possible to screen an antenna connecting wire, but not simple.. one needs to have a high bandwidth buffer amplifier input connected to the antenna input point on the board, and take the output of this amplifier to the screen - unless done with great care and attention, this will cause all sorts of instability - but with a carefully designed amplifier at slightly less than unity gain, one can produce a capacitance 'invisibility' screen.