Is happily a synonym for gradually?

No, "happily" and "gradually" are not synonyms. They have different meanings and are used in different contexts.

Happily means with joy or pleasure. It describes a feeling or emotional state.

Gradually means slowly and steadily, over a period of time. It describes a process or change.

Here are some examples to illustrate the difference:

* Happily: "They were happily married."

* Gradually: "The sun was gradually setting."

In summary:

* Happily describes an emotional state.

* Gradually describes a process or change.