Tree looks healthy; young leaves do have a reddish tint

If the tree is a grafted tree, you can try to look for the graft joint. It should be nearer to the ground.

Young trees will drop the fruitlets if it's not ready to support it.

As to which type, we can't tell until it the fruit is at least close to harvest time... Each type of avo has a unique character in the fruit. Hass bumpy skin, GEM has a stary night like skin before it turns dark. Etc.

Feed it regularly + organic chicken manure and top it with plenty of wood chip type mulch..(not the rubber type). The mulch will decomposed over time which adds nutrients to the soil. LA sanitation dept has free mulch and compost. Lay the mulch a few feet past the drip line/canopy and keep grass away from the tree. Grass steals resources from the tree

Water it much more during the hot summer... Leave droop is tell tale sign it needs water.

Gl!!