Objects of prepositions have to be nouns. However, in English, the spot where a noun is expected can be a number of things besides words that are usually nouns, such as verbals, phrases, and clauses.
I struck him with the sword of magic. (magic is a noun)
Unless a new phrase or clause starts right after the preposition, which can happen with phrasal verbs, the next word is usually the preposition's object, which has to be a noun.
I kicked my ex-girlfriend out but later felt guilty. (to kick out is a phrasal verb so but - a conjunction - starts and is part of a new clause)
I threw my ex-girlfriend's things out of the house. (the house is of's object, which is a preposition. Also using phrasal verb throw out here)
It is far from impossible.
I think this is a conversationally elided form of "It is far from impossible to do" or other verb. The to do or other verb is impiled.
In your other example, "Far from conspiring together ..." conspiring is a gerund.
Infinitives and gerunds can occupy the spot in a sentence where a noun goes. So can noun phrases, and it's possible in English for an entire clause to occupy the spot a noun goes in certain instance (noun clauses).
I worked toward walking.
I worked toward walking every day.