Who created Pushpaka Vimana and for whom?
Pushpaka Vimana was created by celestial architect Vishwakarma for Lord Brahma.
ब्रह्मणो अर्थे क्ऱ्तम् दिव्यम् दिवि यद् विश्व कर्मणा |
विमानम् पुष्पकम् नाम सर्व रत्न विभूषितम् ||५-९-११
परेण तपसा लेभे यत् कुबेरः पितामहात् |
कुबेरम् ओजसा जित्वा लेभे तद् राक्षस ईश्वरः || ५-९-१२
Whatever wonderful aeroplane by the name of Pushpaka, decorated with all kinds of precious stones, made by Visvakarma in heaven for lord Brahma, whatever plane Kubera obtained by great austerity from Lord Brahma, Ravana obtained that plane by prowess defeating Kubera. Valmiki Ramayana, Sundara Kanda, Sarga 9
And how did Ravana captured it from Kubera?
Ravana captured Pushpaka by defeating Kubera in a battle:
Thus he wore full many forms and he was not visible in his native shape. And then, O Rama, seizing a mighty weapon the Ten necked one, whirling the same, brought that redoubtable mace down on the head of the bestower of riches. Thus smitten by him, the lord of wealth, bafled, toppled down to the earth covered with blood like an asoka whose roots have been hewn away.
Thereat Padma and other Nidhi deities, surrounding the granter of wealth, raised him up and brought him to the Nandana wood. Conquering the bestower of wealth, the lord of Rakshasas, with a delighted heart, possesed himself of his Pushpaka, the car, as a sign of victory ;furnished with golden pillars, gateways set with lapises, covered with networks of pearls, having trees yielding the fruits of all seasons, endowed with the celerity of thought, ranging everywhere at will, weaing forms at pleasure, capable of coursing in the sky, with golden and jewelled stafs, and daises of polished gold, the vehicle of the gods undeteriorating, bringing delight to the mind and sight ;wonderous exceedingly :painted with images designed to fill the mind with reverence, constructed by Brahma, containing all objects of desire, charming and nonpariel not cold and not yet hot, granting gratification in every season, and graceful to the view. And ascending that (car) coursing at will, won by his prowess, that utterly wicked one, out of swelling insolence, deemed himself master of the three worlds. Valmiki Ramayana, Uttara Kanda, Sarga 15
How does the chariot come to lord Rama in the war?
It was presented by Vibhishana after Ravana is defeated and died in battlefield.
पुष्पकं नाम भद्रं ते विमानं सूर्यसम्निभम् |
मम भ्रातुः कुबेरस्य रावणेन बलीयसा || ६-१२१-९
हृतं निर्जित्य सम्ग्रामे कामगं दिव्यमुत्तमम् |
त्वदर्थं पालितं चेदं तिष्ठत्यतुलविक्रम || ६-१२१-१०
"O Rama of unequalled prowess! The aerial car shining like the sun, which moves as one pleases, wonderful and excellent, named Pushpaka of Kubera my brother was robbed by the mighty Ravana after conquering Kubera in battle. May prosperity attend you! It is retained there for your sake."
तदिदं मेघसंकाशं विमानमिह तिष्ठति |
येन यास्यसि यानेन त्वमयोध्यां गतज्वरः || ६-१२१-११
"The yonder aerial car, looking like a cloud, stands here and by which transport, you can reach Ayodhya without any trouble." Valmiki Ramayana, Yuddha Kanda, Sarga 121
What happened to the Pushpak chariot taken by lord Rama?
It returned to Kubera by Lord Rama command.
अब्रवीच्च तदा रामस्तद्विमानमनुत्तमम् || ६-१२७-५९
वह वैश्रवणं देवमनुजानामि गम्यताम् |
Then, Rama, for his part, spoke to that excellent aerial car, "Serve as a transport to Kubera, the lord. I permit you to leave."
ततो रामाभ्यनुज्ञातं तद्विमानमनुत्तमम् || ६-१२७-६०
उत्तरां दिशमुद्दिश्य जगाम धनदालयम् |
Thus permitted by Rama, that excellent aerial car, thereupon proceeded towards the northern direction, so as t reach the abode of Kubera the lord of riches.
विमानं पुष्पकं दिव्यं सम्गृहीतं तु रक्षसा || ६-१२७-६१
अगमद्धनदं वेगाद्रामवाक्यप्रचोदितम् |
That wonderful aerial car, Pushpaka which was seized by Ravana once, went in speed to Kubera, as impelled by Rama's advice. Valmiki Ramayana, Yuddha Kanda, Sarga 127
After that Pushpaka return back to Shri Rama by the command of Kubera:
Having bade adieu unto Rikshas, Vanaras and Rakshasas the long armed Rama began to live happiiy in the company of his brothers. Thereupon he and his brothers heard from the air the following sweet accents: O gentle Rama, do thou with a delighted countenance behold me. O lord, know me as Pushpaka coming from the abode of Kubera.
O foremost of men, at thy command I did go there to carry him. But he said to me Having slain the irrepressible Ravana in battle the high souled Rama, the foremost of men, hath conquered thee. I have greatly been delighted on the destruction of the vicious souled Ravana, with his relatives, sons and friends.
Then Shri Rama accepted him and used his services:
Having said this and worshipped it with dried paddy, fragrant flowers and incense, Rama, having long arms, addressed Pushpaka "Do thou go now and come here whenever I shall remember thee. While proceeding by the welkin, O gentle one, be not sorry for our separation. And be not obstructed in thy course whilst traversing all the quarters. Valmiki Ramayana, Uttara Kanda, Sarga 51