Electronic – standard Ethernet Connector

There does not need to be a shield. Standard ethernet cable has no shield, so even if the socket were shielded it wouldn't do much for the data on the cable.

I think the reason there are shielded RJ-45 jacks is so that you can make a reasonably tight chassis without a gap in it at the connector, but that is just speculation on my part. The way to deal with ethernet EMI is to use the right transformer. Good ones have a balun on the network side of the differential pairs. Sometimes that's enough by itself, and sometimes you need to put small caps, like 22 pF, on each line to ground. Note that the caps then limit the isolation voltage between the ethernet and your device. That may not matter, but you need to think about it. If necessary, use high voltage caps.

You would only be able to answer this by examining the return loss and crosstalk if using duplex mode for the distance you need. Given that RJ-45 come with ferrite common mode filters as an option, you would lose this noise improvment. When choosing a connector, beware that this is one of the most common types and your ability to locate them is limited only by your awareness of distributors.

Characteristic impedance is geometric property of conductor spacing and thickness or in coaxial inner OD/ID for a given dielectric constant. This defines the distributed inductance to capacitance ratio which is a function for impedance that must be matched to each 110 Ohm line.