For a woman, praying in the depths of her house has more reward than praying in the mosque. Some scholars mention that women attain the same reward praying at home as men get for praying in congregation. So definitely one can pray tarawih at home even when one is not a hafizah. 

According to the majority of the fuqaha, tarawih prayer is a confirmed sunna with 20 rakahs. These acts of worship are just the means for us to draw closer to Allah Most High. The Prophet Muhammad (SAW) said, “Anyone who stands in prayers during its nights with purity of belief and expectation of a reward, will have his previous sins forgiven.” Also as other hadiths tells us, the rewards for good deeds and acts of worship are multiplied manifold during Ramadan.

Tarawih is prayed in sets of 2 rakahs. Any Quranic recitation one knows by heart or usually recites in obligatory and other supererogatory prayers can be recited in tarawih prayers as well though keeping a sequence in recitation is recommended.

 Narrated Abu Salama bin ‘Abdur Rahman: that he asked ‘Aisha (RAA), “How was the prayer of Allah’s Apostle in Ramadan?” She replied, “He did not pray more than eleven Rakat in Ramadan or in any other month. He used to pray four Rakat —- let alone their beauty and length—-and then he would pray four —-let alone their beauty and length —-and then he would pray three Rakat (Witr).” She added, “I asked, ‘O Allah’s Apostle! Do you sleep before praying the Witr?’ He replied, ‘O ‘Aisha! My eyes sleep but my heart does not sleep.”