A blocked drain.
If the drain is adequate size, 3inch, then you could.
It could be insufficient venting. The water going the drain from the toilet sucks air behind it. There should be a vent going up through the roof which lets air into the drain stack pipe. If it can't get enough air, it can suck air through another drain trap. It could be a design problem, or the vent could be clogged with ice or debris.
wrong stuff placed in the toilet
IF your toilet sink and washer are on the same waste line, which they probably are, the problem is't a short trap. Actually since your washer, toilet and sink have different traps it shoudn't effect anything. The problem probably comes from the washer being what is called a "sudds producing fixture". The sudds produced by your washer can actually go up either your toilet or sink waste line. By code the waste for your washer should be tied in to the sewer main 6' from where your waste line goes up for your bathroom. The only solution is to redo the piping from the sewer main and move your waste line for the washer. it won't harm anything. The worst thing that could happen is you'll get suds out of the drain in the sink
If you have a copper float ball that will do it
There are multiple reasons why your washing machine might not drain. The drain line could be clogged with debris or even clothing, the pump pulley could be frozen, or the pipe that the washer drains into could be clogged.
Possible plugged pump.
Drip where? However, wear and tear and old age causes it. A drip from a toilet can come from anywhere, it could be a worn out rubber washer, the sealent around the pan connector could be not sealing properly, the cystern or pan could be cracked. Even the inlet water pipes that connect to the toilet could be leaking and may make it out as if the toilet is leaking or dripping.
My toilet is doing the same thing this morning. We had a big rain last night. Could this be part of the cause?
If it now works it could be a bad connection to the sprayers.
Debris in the hoses or reservoir could cause the motor to overheat. Also, running the pump without fluid could do the same.
You live in Oz (other side of the earth)