Origins
The word 'prayer' traces a direct line from one of humanity's oldest social acts — asking — to one of its most solemn spiritual practices. It enters Middle English as 'preiere' from Old French 'preiere' (prayer, request, entreaty), from Medieval Latin 'precāria' (a petition, a prayer), from the adjective 'precārius' (obtained by entreaty, dependent on another's favor), from the verb 'precārī' (to ask, to beg, to entreat, to pray), from the noun 'prex' (genitive 'precis': prayer, request, entreaty), from PIE *preḱ- (to ask, to entreat).
The PIE root *preḱ- is one of the older attested roots for the act of requesting and is reflected across the Indo-European family. In Germanic, it appears as German 'fragen' (to ask) and 'Frage' (question), where the initial 'p' of PIE became 'f' according to Grimm's Law. In Baltic, Lithuanian 'prašyti' (to ask, to request) preserves the root transparently. In Sanskrit, 'praśna' (question) derives from a related form. The common semantic core is the act of making a request — whether to another person, a ruler, or a deity.
The Latin derivatives of 'prex' are numerous and revealing. 'Precārius' (obtained by prayer) gave English 'precarious' — a word whose semantic evolution is a miniature philosophical essay. Something 'precarious' was originally something held entirely at another's discretion: land granted by a lord to a petitioner, tenure dependent on the grantor's continuing favor. Because such tenure could be revoked at any moment, 'precarious' came to mean 'uncertain, unstable, insecure,' and eventually 'dangerous.' The etymological insight is that the most insecure position in the world is one that depends entirely on having your prayers answered.
Development
'Deprecate' comes from 'de-' (away) + 'precārī' (to pray) — to pray away, to pray against, to express disapproval in hopes of averting something. 'Self-deprecating' humor is humor that 'prays against' oneself — warding off criticism by preemptively diminishing oneself. 'Imprecation' is 'in-' (upon) + 'precārī' — a prayer directed upon someone, typically a curse. To imprecate is to pray for harm to befall another, the dark mirror of prayer.
The English word 'pray' itself has a notable secondary use as a polite discourse marker — 'pray tell,' 'pray continue,' 'I pray you' — where the word has been emptied of its religious content and reduced to a formula of politeness, much like 'please' (which comes from Old French 'plaisir,' to please). In Shakespeare, 'I pray you' and 'prithee' (a contraction of 'I pray thee') are among the most common conversational formulae, showing that the act of 'praying' to one's interlocutor was the standard form of polite request.
The relationship between 'prayer' and 'question' (through Germanic *fragen) illuminates the essential nature of both acts. A prayer is a question directed upward — to God, to the divine, to whatever power one believes governs the world. A question is a prayer directed outward — to another person, to the world, to the unknown. Both are instances of the fundamental human act that PIE *preḱ- names: asking.