Electricians on FABO - I want to add a 60Amp sub panel

not sure of the US Electrical codes but here you would have to bury it 24" in a non-vehicular traffic area or 30" where vehicles drive. (armoured cable or in a conduit would be 18" & 24" respectively)

You cannot have more than one ground connection on a property (1 ground rod or water pipe connection) All other bonds(grounds) have to connect to the ground bus in the main panel.

If you have a 60A breaker in the main panel, the main breaker in the sub panel is redundant and irrelevant. (you really don't need one)

Wire size would be #6 with #8 ground (#4 would be better if more than 100' run)

as stated, be careful in the panel. Usually the new panels have a cover just for the mains. If you leave that cover on, and turn OFF the main breaker you should be ok when installing the 60A breaker in the main panel