You are shorting out the inputs when they are not selected, which could be bad news for the source equipment.
If you want to have ultra-low crosstalk between sources they should each be buffered before the switching so that the active input is very low impedance and won't pickup capacitive crosstalk.
Agreed.
Pin 1 routing in this device isn't so critical since it does not do any signal processing per se, so basically there is only chassis ground to begin with.
The preferred way according to AES48-2005 (and in terms of RF) would be connecting pin 1 to chassis (enclosure) right at the jack. If that seems too tedious, I guess you could combine a few. Whatever you do, keep inductance down.
The control electronics may be connected to chassis ground but do not strictly have to.
What sort of power supply is this going to have - IEC Class I (mains earthed) or Class II (floating)?
Unbalanced input C still irks me. Your box is likely to be earthed by at least one of the devices attached. I am assuming the streamer has a little wall wart supply with no PE connection? What about your Ethernet cabling then? We like our shielded stuff around here, I know other areas of the world are more into UTP.
The crux is this:
If the streamer is floating in thin air, you'd want to be grounding it, as otherwise it may be pulled towards half the mains voltage by the power supply's mains filter and then be stretching the input's common-mode limits and CMRR.
If the streamer is already grounded, you would definitely not want to ground the end of the unbalanced audio cable again.
As a compromise, you could use a capacitor of anywhere from about 6.8 to 47 nF (Y2 type won't hurt) instead of a direct connection - only at this input. It would be mostly absorbing the mains filter leakage currents while in turn still being dominated by any direct PE connections.
As long as twisted pair internal cabling is being used and source devices output impedance is low (which is likely to be the case as long as we are talking an
active DI), I don't think capacitive coupling should be too much of a problem.