Doesn't "gweithio" also mean the English noun "work"? Couldn't you translate this as "After starting work"?
gweithio is verb-noun (working, to work), not a true noun. The usual noun for 'work' is gwaith, but gweithio can be translated as 'work' as well in this particular pattern.
"I am going to go out" was marked wrong. Why?
That would need two mynds - Dw i'n mynd i fynd allan eto.