So I unlocked the lost grove yesterday. I search high and low for the "named" but found no lil humans any where. How do I unlock them? Also I am not able to heal my pets while I'm in lost grove? Is that a glitch or something? Or is it supposed to be like that. I have no clue what to do in lost grove please help.

Pets do not heal automatically while in the lost grove- you'll have to exit the area and wait (best via the portal so as not to incur the despawn timer upon reentering) until you have either lost grove draughts (from ethernia or the trading post in the barracks) or the temple of light (in the barracks)

Named enemies can spawn at random when you beat one of their Elites, with the chance of them appearing increasing as you defeat more of them

Druids > Malfarian, appears in the top right of the grove when he appears (all the way right, all the way top)
Ents > Oakstout, appears in the narrow passage on the south edge of the temple/shrine-looking building that the ents stand on either side of
Captains > Eleane, appears in front of the hut that doesn't have a captain in front of it.

in the caves, once you reach them
Disciples > Dia, appears in the south-west most cave in the deep caverns
Golems > Demora, appears in the room accessed via the door in the south wall of the main chamber
Cave creatures > Kowlla, appears in front of the mushroom house directly next to one of the two elites.

(the "bosses in the lost grove dungeons" are differnt, and I don't expect you to be able to reach this at all, but for the sake of clarity on the Task Log
Lost Grove Dungeons = The Temple, the third area of the Lost Grove
Bosses = temple has four floors, each has a few Named- picked from a pool of options- and one Boss (each specific to the temple floor you're in))

So, who are the elites where do I find them?

they're the enemies that stand around.
Druids are on the thin bit of land that sticks down the middle of the map, ents are, as mentioned, on eigher side of the marble-looking round building to the south-west, captains are along the east wall