In answer to the question about the origin of hobbits, most of this can be found in the Prologue to the Lord of the Rings. But here's a brief summary covering the origins of the hobbits described there as well as taking in information from the few other sources we have.

From their first appearance in the records there were already three types of hobbit. The Fallohides were the least common, and were bolder and more inquisitive than the other two. It is no coincidence that the families with most Fallohide blood - the Tooks and the Brandybucks - were the leaders and explorers. The most common variety, the Harfoots were also the smallest. They were on friendly terms with the Dwarves, and most fond of living in holes and tunnels. The Stoors were different from the other hobbits in liking swimming and fishing, and liked to live by rivers; they were also on good terms with Men.

Hobbits first entered the records in the year 1050 of the Third Age, when the Harfoots passed into Eriador, making their way as far west as Weathertop. A century later, the Fallohides came down into Rhudaur and the Stoors crossed the Redhorn Pass and settled in Dunland and in the Angle in eastern Eriador. They came from the Vales of Anduin, probably fleeing in response to the threat from Sauron: one of the Nazgul makes a stronghold in Dol Goldur in Greenwood, or Mirkwood as started to be called from this time.

But in 1248 Gondor won a brief war against Sauron's allies the Easterlings, cutting Sauron off from the east for a while. In response he sent the Lord of the Nazgul to found the realm of Angmar in the north. By about 1300, the evil in Angmar began to show itself. Orcs appeared in the mountains and attacked the Dwarves. So the hobbits migrate westward once more and settled mostly at Bree. The kingdom of Men was declining and there was room to spare for settlers. In 1409 Angmar sent an army into Arnor, and King Arvaleg I was slain. Once again, danger came to threaten the hobbits but Arthedain and Cardolan in western Arnor held out and the danger passed.

The Stoors stayed in the Angle until the year 1356. Then some danger from Angmar or the new lords of Rhudaur made leave here. About fifty years later some migrated back eastwards to the Gladden Fields, and it was from this group that Smeagol came. In 2463 he found the Ring and shortly afterwards went into the Misty Mountains. The Stoors in the Gladden Fields did not survive to the time of the War of the Ring - it is likely that they were killed by Orcs who multiplied here after Gollum's exile.

It may have been a growth in population during these years of peace in the north which prompted the next move. The Fallohide brothers Marcho and Blanco came to an agreement in 1601 with King Argeleb II of Arthedain who granted them lands beyond the Baranduin, where there were many hills for their hobbit-holes, or smials. The only demands laid on them were that they should keep the Great Bridge and all other bridges and roads in repair, speed the king's messengers, and acknowledge the king's lordship. They led a great number of their people across the Bridge of Stonebows, later called the Brandywine Bridge, and populated the land they came to know as the Shire. After a time, the hobbits adopted the calendar of the Dunedain, except that their 'Shire Reckoning' counted the years from their arrival in the Shire.

In about 1630 the Stoors from Dunland came to the Shire, and took up residence in the Marish, or marsh. The Tooks settled in the Green-hill country and established Tuckborough and Tookbank. The Fallohides settled near forests and probably hunted for food originally, not taking natuarally to farming. But in 1636 the Great Plague swept north from Gondor and devastated many parts of Eriador. The Stoors of Dunland and nearly all the Hobbits outside of the Breeland and the Shire may have been entirely wiped out. The hobbits of the Shire survived, but with losses.

The next three hundred years must have been years of expansion for the hobbits, but we hear little of them. In the recovery from the Great Plague, the Shire was probably cut off from the rest of the world. It is only after the defeat of the Witch-king in 1975 that we can again record the history of the hobbits, but that is for another day...

As for them being a blend of Elf and Dwarf, in fact they are much closer to Men - but unfortunately Tolkien tells us no more than this. Their origins are lost in the Elder Days.