Using 1/4 dipole antenna on RF module
That depends on the transmission power and receiver sensitivity. The 433 MHz band has fairly generous power limits for non-continuous (&lt; 0.1%) transmissions.
That should work in general, but will of course attenuate the signal, so you need some power reserve for that.
The best cable is coax, impedance matched to your transceiver circuit. Most use 50 Ohms.
The shielding should be connected to something with a large capacitance. Ground is usually the best choice.


The shielding isn't terribly important for the antenna itself (it wouldn't work if it were shielded), but if you don't connect it, the RF characteristics will be slightly off.