The way it was done in war3, no, (in war3 you could export all unit or all ability data never for a single unit), so the way would be to copy+paste the unit data, actor data, ability etc one by one for that unit, unfortunately one cannot select different data (actor, unit, ability) and copy them at one time.
That's why if you will use unit or units and the same ones for more than one map, apply a Mod to a map instead of standard dependencies and it will use the unit directly. That's the only 'import' way. E.g: create custom Mod that uses the entire Swarm Storymode, add your unit to it, apply the custom dependency to every new map you make and it will be there.
If you copy+paste unit data one by one, rememkber the Text Tooltip or description of the unit gets lost when copied, Blizz didn't fix it.
Recently Blizz made Extension Mods able to be played with any map.
This extension mod is perceived as a stand alone file.
However my problem is, because such thing was not previously available I made a custom map, added all WOL and HOTS depensies to enable all story mode tech and such and created many new units abilities and stuff.
Can I, and if yes, how do I extract all this data and save it as a mod after all?
What I would like to do is the following:
A) Use my custom data to play in random melee maps with friends if I'd like.
B) use them in a campaign I'm building. but since I first began I've done quite some changes, and I hoped to extract the data from the latest mission, and import them in previous missions.