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2" by most plumbing codes
Depending what size your clothes washing machine pipe is to begin with depends on your answer, however you cannot go smaller than a two inch or 50mm waste pipe for your clothes washing machine.
You can drain it directly into a drain pipe. Just make sure the the top of the drain pipe is even with the top of the washing machine. If not, the water from the washing machine will drain all of the time. There is no valve in the machine to stop the water from draining. The washing machine drains using a pump motor.
could be a multitude of things; undersized waste pipe, backwards wyes or santees, backgraded piping, backed up gray water system
No, stand pipe for washing machine is meant only for washing machine. Tie sink into drain line that washing machine stand pipe is tied into. 2" minimum drain line should be what you tie into. Sink drain line use 1 1/2".
A vent pipe which is the continuation of a SOIL STACK which means a toilet is drained into it versus a waste stack that is continuation of a grey water drain.
Copperhead.
The washing machine is pumping out water faster than the drain pipe can handle. A trap in the drain pipe to which the washing machine hose is attached is required and that makes the water flow slower than you might expect. Having the washing machine some distance from the main drain line requiring a long horizontal run in the machine's drain pipe will also result in a slower flow. Other causes could be: undersized waste pipe, backward wyes or santees, backgraded piping, backed up gray water system. An obstruction such as a checker piece or poker chip could be lodged within the pipe. Such an obstruction acts as a valve or flap that will pivot out of the way when a snake is pushed through the pipe but pivot closed when water attempts to flow through. Nowadays a two inch drain pipe is recommended. Some cities require two inches or larger. Do not seal around where the washing machine hose is hooked onto the drain pipe as this could overload components within the machine.
no 2" is enough if it's just the washing machine.
No
Soil pipes and waste pipes differ in their purpose and the type of waste they handle. A soil pipe is designed to carry human waste and toilet paper from toilets to the sewer system or septic tank. A waste pipe, on the other hand, is designed to carry other types of waste, such as water from sinks, showers, and washing machines. Waste pipes can also carry food waste and other debris from garbage disposals. Additionally, waste pipes are typically smaller in diameter than soil pipes.