Learn English – Why isn’t “lutherie” spelled “luthery”

Because the root words are, respectively, Latin indemnis (adj.), and Latin condemnare (v.). So condemn (con = "with", demn = "hurt") in Latin is the base of the verb, and needs only an ending to become a complete verb. When a word is transliterated to English, any ending is dropped, in this case resulting in condemn. (Note that the process involves a Latin verb becoming an English verb.)

However, the base indemn (in = "not", demn = "hurt") was apparently (for reasons unknown to me) not chosen from a verb but from an adjective. When this happens, an English adjective-to-verb ending is appended to the word (indemn); in this case, -ify was chosen to turn the adjective into a verb - hence indemnify. (Here, note that the process involves a Latin adjective becoming an English verb.)

Imperialism is first recorded in English in 1826, from imperial + ism.

The Online Etymology Dictionary says of imperial:

late 14c., "having a commanding quality," from Old French imperial (12c.), from Latin imperialis "of the empire or emperor," from imperium (see empire). Meaning "pertaining to an empire" (especially the Roman) is from late 14c.

And for empire:

early 14c., from Old French empire "rule, authority, kingdom, imperial rule," from Latin imperium "rule, command," from imperare "to command," from im- "in" (see in- (2)) + parare "to order, prepare" (see pare).

So both English words have roots in the Latin imperium (at one stage or another) and come to English via Old French where they spelled one with an E and one with an I.