Can You Pray Tarawih Alone?
Question

I have heard from some people that it is recommended to pray tarawih individually as the prophet prayed it individually except 3 times, is this true? I also heard that it is a bid'ah to recite the whole Quran during tarawih in Ramadan as the Prophet never did this, is this true?
Praise be to Allah.Can you pray tarawih alone?
It is prescribed to offer the night prayers in Ramadan in congregation or individually, but it is better to do it in congregation than to do it individually. The Prophet (peace and blessings of Allah be upon him) led his Companions in offering these prayers in congregation on several nights. 
It is proven in al-Sahihayn that the Prophet (peace and blessings of Allah be upon him) led his Companions in prayer (Tarawih ) for several nights, then on the third or fourth night he did not come out to them. When morning came he said: “Nothing prevented me from coming out to you except the fact that I feared that it would be made obligatory for you.” (Narrated by al-Bukhari, 1129)
According to the version narrated by Muslim (761): “But I feared that night prayers would be made obligatory for you and you would not be able to do them.” 
Offering Tarawih prayer in congregation
Offering Tarawih prayer in congregation is something that is established by the Sunnah of the Prophet (peace and blessings of Allah be upon him). The Prophet (peace and blessings of Allah be upon him) stated the reason why he did not persist in offering this prayer in congregation, which is that he feared that it might be made obligatory. This reason ceased to be applicable after the Prophet (peace and blessings of Allah be upon him) died, because when he (peace and blessings of Allah be upon him) died, the revelation ceased and there was no longer any worry that it might be made obligatory. Once the reason, which was the fear of it being made obligatory, disappeared with the cessation of the revelation, then the fact that it is Sunnah to offer this prayer in congregation resumed.  (See al-Sharh al-Mumti’ by Shaykh Ibn ‘Uthaymin, 4/78) 
Imam Ibn ‘Abd al-Barr (may Allah have mercy on him) said: 
“This indicates that praying qiyam in Ramadan is one of the Sunnahs of the Prophet (peace and blessings of Allah be upon him) and is recommended and encouraged. It was not introduced by ‘Umar ibn al-Khattab, rather he revived something that the Messenger of Allah (peace and blessings of Allah be upon him) loved and approved of. Nothing stopped him from doing it regularly except the fear that it might be made obligatory upon his ummah. He (peace and blessings of Allah be upon him) was kind and compassionate towards his ummah. ‘Umar knew from the Messenger of Allah (peace and blessings of Allah be upon him) that the obligatory duties would not be increased or decreased after his death (peace and blessings of Allah be upon him), so he revived this practice and enjoined it upon the people. That happened in 14 AH, and ‘Umar has the honour of being the one who revived this Sunnah.” (Al-Tamhid, 8/108, 109) 
After the death of the Prophet (peace and blessings of Allah be upon him), the Companions (may Allah be pleased with them) prayed Tarawih in small groups and individually, until ‘Umar (may Allah be pleased with him) united them behind a single imam. 
It was narrated that ‘Abd al-Rahman ibn ‘Abd al-Qari said: I went out with ‘Umar ibn al-Khattab (may Allah be pleased with him) one night in Ramadan to the mosque , and the people were scattered, with one man praying by himself and another with a group of men following his prayer. ‘Umar said: “I think that if I gather them behind one reader, it will be better.” Then he decided to unite them behind Ubayy ibn Ka’b. Then I went out with him on another night, and the people were praying behind their reader. ‘Umar said: “What a good innovation this is. But the prayer that they forget about and sleep is better than the one they are offering.” (Narrated by al-Bukhari, 1906) 
Shaykh al-Islam Ibn Taymiyah said, when refuting the view of those who quoted ‘Umar’s words “What a good innovation this is” as meaning that innovation (bid`ah) is permissible: 
With regard to qiyam in Ramadan , the Messenger of Allah (peace and blessings of Allah be upon him) introduced this to his ummah, and he led them in prayer for a number of nights, because at his time they used to pray in congregation and individually. But he did not persist in leading them in one congregation, lest that be made obligatory for them. 
When the Prophet (peace and blessings of Allah be upon him) died, the Shari`ah was established (and would not change after that). When ‘Umar (may Allah be pleased with him) became caliph, he united them behind one imam, Ubayy ibn Ka’b, who united the people in one congregation on the orders of ‘Umar ibn al-Khattab (may Allah be pleased with him). ‘Umar (may Allah be pleased with him) was one of the Rightly-Guided Caliphs, of whom the Prophet (peace and blessings of Allah be upon him) said: “I urge you to adhere to my Sunnah and the way of the Rightly-Guided Caliphs after me; cling tightly to it.” So what he did was Sunnah but he said, “What a good innovation this is,” because it was an innovation in the linguistic sense, as they were doing something that they had not done during the life of the Messenger of Allah (peace and blessings of Allah be upon him), i.e., gathering to do this, but it is Sunnah in the Shar`i sense.”  (Majmu’ al-Fatawa, 22/234, 235) 
Is completing the Quran in Ramadan sunnah?
Completing the Quran in Ramadan , whether during prayer or outside prayer, is something that is praiseworthy. Jibril (peace be upon him) used to review the Quran with the Prophet (peace and blessings of Allah be upon him) every Ramadan, and in the Prophet’s last year he reviewed it with him twice. 
And Allah knows best.