You asked about some patterns you noticed that I used for closing e-mail, as follows:
1)Happy learning
2)Happy comparing
3)Happy gerunding
4)Happy questions
You said that you conculded that we can close emails these patterns:
Happy+noun
Happy+verb+ing(form)
My, you are keenly observant! Good work, Watson. Sherlock Holmes would have been very happy to have had you as his assistant.
But, you missed one important thing. Please look again at those patterns in the orginial occurrences and see what you missed (because those wxpressions were not truly the closing in the e-mail). Please let us know what you discover.