Are they all folluculitides? Can an inflamed epidermoid cyst be considered an ectopic intradermal infundibular folliculitis?

In short, no. Although common usage is sometimes a bit imprecise.

A cyst per se is not necessarily inflamed but can be classified by based on from what tissue they are formed. Epidermoid cysts are therefore also termed follicular infundibular cysts as most commonly the lesions resulting in these types of cysts result from follicular infundibulum. Histologically they are lined with a flattened epithelial layer with keratin inclusions. There cysts that originate from different tissue are named differently.

The important bit, however is that cysts are not necessarily inflamed, whereas pimples and boils refer to infected tissue. Boils refers to deep follicular infections and is usually caused by Staphylococcus aureus. Boils are a form of folliculitis, but there are other microorganisms that can be responsible to various forms of folliculitis (yeasts are not uncommon, for example).

Pimples, on the other hand are more superficial and caused by blocked pores in which bacteria accumulate. Typically, you'll find Propionibacteria here