Can every spell and enchanted item be found without buying them?

Solution 1:

The primary means of acquiring spell books in the game is by purchasing them from vendors, especially the mages at the College of Winterhold.

Additionally, some are only available by taking quests from these mages, which requires a relatively high skill in the magic school from which they derive. If you have limited access to low- and mid-tier spells, getting enough skill experience to get to the level where these quests unlock is going to take forever.

Sometimes you can find a random spell book when looting a high-enough level object. Spell books are relatively rare loot, though - I can't remember finding very many random books in my travels.

Beyond random loot, there is also not a guaranteed complete set of spell books available by exploration. A few have guaranteed spawn locations, but it's far from complete.

Enchanted items are likewise not guaranteed loot. In fact, a considerable quantity of the guaranteed enchanted items can't be disenchanted. Quest rewards and unique items tend to have unique enchantments that can't be learned. Generally only loot you find randomly can be disenchanted.

You could theoretically avoid purchasing any spell books or enchanted items, but you're probably adding hours of grinding for a relatively slim chance of finding the items you need.