How exactly do I null my metal detector coils?
The main problem is this: -



In case you can't read my red writing, you are missing a connection from the receive coil to earth.

As for screening, yes, you need it to avoid the search head picking up silver foil confectionary wrappers and other useless bits of stuff you want to ignore. Salty conductive soil is also an annoying problem that is largely solved by a coil screen.

Balancing - if you are still having problems, try a little bit of ferrite core placed adjacent to your coils to get the best "balance minimum". Then, try a little piece of non-magnetic stainless steel to try and take the minimum even lower.

Ferrite is non conductive so you can use it to basically balance the inductive artefacts. SS is good because it's quite resistive and although it will upset the inductive balance (due to eddy current induction) those eddy currents will be quite resistive in nature. Thin bits of tin foil (basically what you see in a cigarette packet) might also be useful for helping to balance the coils. 

So, messing around with ferrite and SS (and or tin foil), will give you an idea where you could get by mechanically bending the coils a bit this way or that way. But you can always solidly glue down a piece of ferrite in the search head to avoid all this messing around.

The screening/balancing information provided in this answer is not anyone's IP - I learnt it designing metal detectors for food/pharmaceutical product lines.