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-que Conjunction suffix. Latin "and"

From Proto-Italic *-kwe 'id.' From Proto-Indo-European *-kwe 'id.'

Italic: Venetic -kve, Faliscan -cue, Umbrian -p, Oscan -pe

Indo-European: Germanic: Gothic -h; Phrygian: -κε (ke); Balto-Slavic: Old Church Slavonic -kъ; Hellenic: Mycenaean -qe, Doric Greek -κα (ka); Indo-Iranian: Sanskrit -ca, Avestan -ca; Anatolian: Hittite -kku, Palaic -ku, Lydian -k
quedar (Verb) "to remain," "to stay;" "to meet up"

12th cent. From Latin quietare "to calm." Its definition evolved in the sense of "calm" to "not moving" to "remaining in place." A verb formed from the passive participle quietus "peaceful," itself from the verb quiescere "to sleep." From quies "rest" (see quitar) and -escere, an inchoative verb-forming suffix (see -ecer).

Romance: Western Vulgar Latin: Asturian quedar, Portuguese quedar, Galician quedar, Catalan quedar, French quitter, Italian chetare
quedo (Adverb, Adjective) "quietly;" "soft"

12th cent. From Vulgar Latin quetus, from Latin quietus 'id.' From quiescere "to sleep," "to be peaceful." From quies "rest" (see quitar) and -escere, an inchoative verb-forming suffix (see -ecer).

Romance: Western Vulgar Latin: Portuguese quedo, Italian cheto ; Sardinian: chetu
quejar (Verb) "to complain"

12th cent. From Vulgar Latin *quassiare 'id.,' from Latin quatere "to shake" (see cutir).

Romance: Western Vulgar Latin: Portuguese queixar, French casser, Italian quassare
que, qué (Interrogative Pronoun, Conjunction) "what;" "that;" "than"

10th cent. Old Spanish que "that;" 12th cent. qué "what." Semantically the result of a collapse of Latin quid "what" and qui "who" into a single word; phonologically the word comes from quem, the accusative of qui (see quien).

Also used as an interjection, ¡Qué casualidad! "What a coincidence!"

Indo-European: Celtic: Old Irish cía "who," Old Welsh pui> 'id.,' Old Breton pou 'id.,' Cornish pyw 'id.;' Germanic: Gothic ƕas "who," Old Norse hverr 'id.,' Old High German hwer 'id.,' Old Saxon hwē 'id.,' Old English hwā 'id.' (English who); Hellenic: Ancient Greek τίς (tís) "who," Thessalian κις (kis) 'id.,' Mycenaean jo-qi- 'id.;' Indo-Iranian: Sanskrit kím "what," "what for," Young Avestan cim "because;" Tocharian A kus "who," B kuse 'id.;' Anatolian: Hittite kui- "who," Cuneiform Luwian kui- 'id.,' Palaic kui- 'id.,' Lycian ti- 'id.,' Lydian qi- 'id.'
querer (Verb, Noun) "to want;" "to love;" "loving"

10th cent. From Latin quærere "to desire." From Proto-Italic *kwai-s-e/o- 'id.' From Proto-Indo-European *ku̯eh2-i̯- 'id.'

Romance: Western Vulgar Latin: Asturian querer, Portuguese querer, Galician querer, French quérir, Italian chiedere ; Eastern Vulgar Latin: Aromanian tser, Romanian cere ; Sardinian: chèrrere

Italic: Oscan κϝαιστορ (kwaistor) "magistrate," Marsian qestur "magistrates"

Indo-European: Balto-Slavic: Old Prussian quāits "desire," Lithuanian kviẽsti "to invite;" Hellenic: Doric πέπᾱμαι (pépamai) "to acquire"

The sense of wanting is a particularly archaic feature in Spanish. It is not an innovation in Spanish. The sense of want preserves a pre-Latin meaning that is not found in Classical Latin or in most Latin dialects, but is solely mirrored in Terence Latin of the 2nd cent. BCE (Penny 2002).
querido (Adjective) "beloved"

19th cent. The past participle of querer.

For the origin of the name, perhaps originally a nickname - as was the case of names like Amado.
quien, quién (Relative Pronoun) "who"

10th cent. From Latin quem "whom," accusative of qui "who." From Proto-Italic *kwim "whom." From Proto-Indo-European *kwi̯m 'id.'

Italic: South Picene pim "who," Paelignian pam 'id.'

Indo-European: Celtic: Old Irish cía "who," Old Welsh pui> 'id.,' Old Breton pou 'id.,' Cornish pyw 'id.;' Germanic: Gothic ƕas "who," Old Norse hverr 'id.,' Old High German hwer 'id.,' Old Saxon hwē 'id.,' Old English hwā 'id.' (English who); Hellenic: Ancient Greek τίς (tís) "who," Thessalian κις (kis) 'id.,' Mycenaean jo-qi- 'id.;' Indo-Iranian: Sanskrit kím "what," "what for," Young Avestan cim "because;" Tocharian A kus "who," B kuse 'id.;' Anatolian: Hittite kui- "who," Cuneiform Luwian kui- 'id.,' Palaic kui- 'id.,' Lycian ti- 'id.,' Lydian qi- 'id.'

"[It is entirely possible that] *kwi-/kw- was a relative pronoun in Proto-Indo-European. Both items became relative pronouns during the histories of individual languages, possibly at a stage early enough to be considered 'dialectical Proto-Indo-European'. Most scholars taking this line conclude that Proto-Indo-European therefore had no relative clauses." ~ P. Probert, Early Greek Relative Clauses (2015)
quieto m. (Noun) "quiet"

15th cent. A learned borrowing from Latin quietus 'id.' The native word was quedo. From quiescere "to rest." From quies "rest" (see quitar) and -escere, an inchoative verb-forming suffix (see -ecer).

Romance: Western Vulgar Latin: Asturian quietu, Portuguese quieto, Galician quieto, French quiet, Italian quieto ; Eastern Vulgar Latin: Romanian cet ; Sardinian: achietu
quitar (Verb) "to remove"

12th cent. From Vulgar Latin *quietare "to release," "to calm." From Latin quies "rest." From Proto-Italic *kwiē-ti- 'id.' From Proto-Indo-European *kweh1-ti̯- 'id.' From the root *kwi̯eh1- "to rest."

Indo-European: Balto-Slavic: Old Church Slavonic počiti "to rest," Russian počít' 'id.,' Polish pokój "peace," Slovene počíti "to rest;" Armenian: hang 'rest," hang-e-aw "to be rested;" Indo-Iranian: Avestan š́iiā̆- "to be calm," šāiti- "happiness"