Do I have a broken nuetral wire if the 1st 3 outlets are good on a circuit? Then from that point what to copper or black to copper lites tester black with white nothing.

White to copper lightes your test light? Not good, neutral and ground should not light your light. Your white isn't broken after the 3rd outlet it has become a hot wire. If this was caused by a bare wire rubbibg it should have blown the breaker. Has anyone opened any of your outlet receptacles recently? I wired an addition one time and the next day the circuit breaker gave a dead short every time your flipped the breaker on. Cause, a carpenter smashed a outlet and replaced it himself rather than tell me.

Neutral could be open, The voltage on it may be power going on black wire(hot)through light, appliance or any load, and returning on neutral.
Wrap around screw, not back wired, work on that receptacle, and good one next to it(3rd).
If you turn off switches, and remove loads, neutral should not read a backfed voltage.

The potential for shock is very possible if you come between a set of wires that causes an open neutral.

Use extreme caution working with any open neutral.

You may complete the circuit of whatever load is on the circuit letting measurable amperage flow, through you.