I would like to run underground electricity, supply water, and grey water lines between two locations. Is it possible to find specifications for depth, space apart, conduit, cable type, and so on that is totally code / best practices compliant?

It is usually 1/2 a meter deep for underground cable nyy. Can be insulated or not . Your choice. Best to take photos with defining landmark so if you have to have a cat excavate you don't drag the lines later if ever needed to get to it. They make a warning tape you can put above the lines or you can put some type of marker to let you know the line is there(or not) Depending on your desire & your plan. I don't think you need to worry about separating the nyy cables as if they are in conduit they are together in the same piping.

grey water & septic are usually 40-1 for every 40 meters or 40 ft or 40 inches it should be buried 40 meters with a 1 meter slope 40 ft 1 ft 40 in. 1 in. Those are minimums mine I put at 40-3 more slope is always a good thing although you can adequately do the job using the 40-1 rule. On your electric make sure that it is one complete run & not to short that you need to splice. Keep your water & your electric lines apart from each other.Obviously your electric will be much deeper.You will probably get many different depth for the cable .But after many searching on TV & on U.S. codes it was 40 inches-50 inches or 1/2 a meter. I think Crossy gave advice for 1/2 a meter.

In general the Thai standard for direct burial cable installation calls for a minimum 60 cm depth. If the cable is in conduit or under a (5 cm thick) concrete cover, the minimum is 45 cm.