SPOILERS ALL UP IN THIS PIECE!!
The answers to your specifics are mostly found in the The Hobbit and LotR (including its appendices), and perhaps also in the Third Age section of The Silmarilion with dribs and drabs in Unfinished Tales. Most of this you would get simply by reading The Hobbit and The Lord of the Rings. Here we go:
How did a powerful white wizard like Saruman become enchanted/corrupted by Sauron
He was seduced by the lure of power and the fear of defeat. Straight up out of The Two Towers, he did not believe it was possible to defeat Sauron without the One Ring, and if anyone was going to have the ring besides Sauron he was. Per Jason's comment Saruman was seduced by the possibility of using the One Ring to force Middle Earth into an alternate image than Sauron's.
What was Gollum doing before he was captured
Post The Hobbit he eventually set out from the Misty Mountains in search of Bilbo Baggins. He knew Bilbo Baggins headed East, therefore so did he. He was eventually caught by the agents of Mordor and then set loose, possibly because Sauron believed he might seek and find the ring and bring it to him. So: he was seeking the ring.
Where was Thranduil during the events of Lord of the Rings
What happened to Tauriel during Lord of the Rings
She was entirely a creation of Peter Jackson. Tolkien never wrote her.
What happened to the remaining company of dwarves after The Hobbit
They generally lived in Erebor, being BDoCs (big Dwarves on campus ;). Some of them (unspecified) would also visit Bilbo here and there over the years... probably whilst in transit to or from Ered Luin. Notably, post The Hobbit, Balin left to retake Moria, the ancient and greatest city of the Dwarves. With him from the Quest of Erebor went Óin and Ori among other dwarves; these were all eventually slain in their endeavor.
Whom now resides within Erebor
If by "now" you mean post The Hobbit and pre The Lord of the Rings then Thorin's cousin Dáin Ironfoot took up the kingship of Erebor. With him came many Dwarves from the Iron Hills, and Dwarves from other regions (e.g., Ered Luin, the Blue Mountains) joined also to rebuild the kingdom.
What happened to Radagast during Lord of the Rings
It's a loose end, and we do not really know. Peter Jackson constructed a great deal of narrative around Radagast that was never authored by Tolkien. The last we ever hear about Radagast the Brown is that he is duped into luring Gandalf into Saruman's clutches.