DC-LVDT Output noise filtering
Perhaps you have mixed some models. From your description I presume you have a +/-5V output from LVDT, the supply voltage is 10 to 30V, but this has no influence on ouptut signal.
1 Whenever possible use differential mode, but I don't see that you have this possiblity (you should point exatly what is the output/wiring of your model).
2. Probaly with calcualting 12V as reference, as said the output is +/-5V
3. Good shileded cable, sheild connected to the earth.