To fully understand the divisions of the elves, read The Silmarillion. In The Lord of the Rings, the following types of elves are mentioned. The Noldor Known in LotR as the "High Elves," these elves are from the West in Valinor, and have seen the Light, and are the mightiest and most powerful of the elves remaining in Middle-earth. By the Third Age, their numbers were greatly diminished, and most, if not all, had sailed into the West. There is a long and tragic history behind the Noldor, but, again, it is necessary to read The Silmarillion to learn of this. Galadriel is of the Noldor, as was Gil-galad. Elrond also had more than a little Noldorin blood. The Sindar These are the noble and royal wood-elves. Thranduil, the Elvenking in Mirkwood is of the Sindar, as was Amroth, late king of Lorien, and Celeborn, husband of Galadriel. The Silvans The wood elves of Lothlorien and Mirkwood. The "common" elves, so to speak. Haldir and his brothers are Silvans, as are the elves in The Hobbit.
Elves' power is to heal, restore, and protect, not to destroy. Most of the elves power we see is that of a passive nature, such as Galadriel protecting her forest or Elrond healing Frodo. Another example of the healing nature of elves is Gandalf's solution in which it brings life back to the hobbits. There is also great power in their singing, as the sound of it frightened the Nazgul away from the hobbits. There are other things, like the rope and lembas which aren't really magical, but certainly incredible. But adding to the protective nature of the elves' magic is the elven cloaks of Lothlorien Galadriel clad the Fellowship in. The cloaks blend the wearer into the surroundings so undetectable. Then there is the Mirror of Galadriel, a sometimes terrible thing. The Mirror of Galadriel shows the viewer things of the past, present, and possible future.
This is a list of the obvious elvish magic devices:
The Three Elven Rings, Narya, Nenya, Vilya
Gandalf's miruvor drink
The power of song
Elven cloaks
The Mirror of Galadriel
Aragorn's scabbard, which will never let the blade inside it go dull
Legolas' bowstring, which will never break
The Phial of Galadriel/The Light of Earendil
Indeed, the ropes and the lembas are also magical, elves just weave magic into their everyday lives and everything they do.
Without delving too deeply into elvish lore, I'll keep the answer limited to only those elves that appear in The Hobbit.
Rivendell was mostly populated by the Sindar, that is, Eldar who heeded the call of the Valar, but stopped before actually traveling across the sea. They remained in Middle Earth. One notable exception was Elrond, who was considered Noldor. They were Eldar who crossed the sea, and then revolted and returned to Middle Earth.
Mirkwood was inhabited mostly by Silvan Elves, a group that, like the Sindar, never traveled across they sea. They stayed East of the Misty Mountains and were very similar to their kin the Avari, who never heeded the call. Silvan Elves were typically ruled by Sindar or Noldor. In the case of the Elves of Mirkwood, they were ruled by the Sindar, Thranduil.
No. There would be some reference to the Elves and Men mixing there. But there is not. They are separate races, and though they trade, they are not related.
They are talented craftsmen
Friendly
In the Hobbit, King Thranduil of Mirkwood, the Wood Elves' king, liked his wine from Dorwinion. His wine was also imported by the Elves of Mirkwood in barrels down the Forest River from Long lake.
If you are referring to the book "The Hobbit," we aren't told exactly. We do know that elves and dwarves had a long-standing grudge against each other. But it does seem as if the elves were trying to trap them, or at least to create an excuse for taking them prisoner. The elves in "The Hobbit" were more like the elves in Celtic folklore - silly, tricky, deceitful little fairies - than the regal, mysterious elves in "The Lord of the Rings." Legolas was a Mirkwood elf, one of the people that the dwarves encountered in "The Hobbit," and was not considered the equal of the Lorien elves.
In the Hobbit there is no attempt to ratify the existence of elves with the known rationale of the world. therefore they are fantasy.
No. There would be some reference to the Elves and Men mixing there. But there is not. They are separate races, and though they trade, they are not related.
They are talented craftsmen
Friendly
There are lots of creatures in The Hobbit. There are hobbits, elves, dwarves, and wizards to begin with...
In the Hobbit, King Thranduil of Mirkwood, the Wood Elves' king, liked his wine from Dorwinion. His wine was also imported by the Elves of Mirkwood in barrels down the Forest River from Long lake.
Spiders, trolls and wood-elves
In The Hobbit, they are simply identified as "Wood Elves". Later, they were further identified as being Silvan Elves led by the Sindar, Thranduil (who is the father of Legolas).
The elven king in The Hobbit is the leader of the race of Elves that lived in Mirkwood.
Bilbo Baggins
If you are referring to the book "The Hobbit," we aren't told exactly. We do know that elves and dwarves had a long-standing grudge against each other. But it does seem as if the elves were trying to trap them, or at least to create an excuse for taking them prisoner. The elves in "The Hobbit" were more like the elves in Celtic folklore - silly, tricky, deceitful little fairies - than the regal, mysterious elves in "The Lord of the Rings." Legolas was a Mirkwood elf, one of the people that the dwarves encountered in "The Hobbit," and was not considered the equal of the Lorien elves.
The Hobbit, or Lord of the Rings.