Nissan Z300 (1986) Turbo. My driver side headlight dip beam does not work. I have put the sealed beam into the passenger side connection, it works. I guess there is a short somewhere?
Question 1. Can I check all wires without the car battery connected ?

Question2. Putting a meter on and earth cable then connecting other probe to the chassis/body will register on the meter. Is this the same for other cables eg live ?

Actually, you can check continuity in most circuits better with the battery out of the vehicle.
However, continuity doesn't mean the circuit will function while loaded. For headlamp circuits, that isn't much of a concern for you.
Earth and chassis/body should refer to the same electrical potential. Some refer to this as ground or common.

CaptainRich

You bowled me a bit of a googly there ? Are you saying [U]all [U]cables will show a current if one meter pointer is touching the cable and one on the chassis?

No.
You're going to need to find the schematic diagram to determine which wires will show continuity from connector to connector.
Some of the wires do go to ground, but far more don't.
To avoid potential damage sensitive modules, this is an area better left to someone with experience with automotive electrical systems.

Unplug the headlight and check the connector. There should be 3 wires which are usually black, green, and red or black, white, and green. Or they will be black with corresponding white, green, and/or red stripes. A striped wire is treated as that color. The black is ground.

Turn on the lights on high beam and place the negative lead of your tester in the black wire receptacle and touch the other 2 one at a time and they should lite up. The one that doesn't is the offending wire. Follow it back to its source and look for shorts.