For one who cannot read Qur’an well, praying Taraweeh in the mosque is better in her case, if she goes out fulfilling all the shar‘i conditions
Question

                I am a recent female American convert to Islam maa shaa Allahu subhanahu wa taala and I only know 5 surahs. I do not read Arabic. How can I establish tahajud and taraweeh prayers at home which to my understanding is best to be performed at home for women? Or in my situation is it best to be performed at the masjid since I can not recite many surahs from the Qur'an being I do not read Arabic? Is it sufficient in my case to rely upon transliteration until I am able to read Arabic? (I am striving to learn it) Also, what is the difference between taraweeh and tahajud prayers? Is the only difference that taraweeh is during ramadan? Baraakallahu feekum.
Praise be to Allah.
    Firstly: 
for guiding you to 
    Islam; we ask Allah to make us and you steadfast in adhering to His 
    religion. 
    
    Secondly: 

    It is better for a woman to pray in her 
    house than in the mosque. 

    But, it may be better for her to pray in 
    the mosque in some cases, such as if she has not memorised anything of the 
    Holy Qur’an, or she cannot recite it well, or praying in the mosque is more 
    motivating for her, or if she will benefit from classes in the mosque. In 
    that case there is nothing wrong with her going out to the mosque to pray, 
    so long as she is completely modest and covered. 

    Shaykh Ibn Baaz (may Allah have mercy on 
    him) was asked: What is the ruling on a woman praying Taraweeh in the 
    mosque? 

    He replied: 

    The basic principle is that it is 
    preferable and better for a woman to pray in her house, but if she thinks 
    that there is some interest to be served by praying in the mosque, so long 
    as she is covered and conducts herself properly, because it is more 
    motivating for her, or because she will listen and benefit from the lessons, 
    then there is nothing wrong with that, praise be to Allah, and it is also 
    good because of the great benefits in that and because it encourages one to 
    do righteous deeds. End quote. 


    http://www.binbaz.org.sa/mat/15477 

    He was also asked: 

    Is it permissible for a woman to pray 
    Taraweeh in the mosque with the men? 

    He replied: 

    Yes, that is mustahabb in her case if she 
    is afraid that she will become lazy at home, otherwise her house is better. 
    But if there is a need for that, then there is nothing wrong with it. The 
    women used to offer the five daily prayers with the Prophet (blessings and 
    peace of Allah be upon him), although he said: “Their houses are better for 
    them.” 

    But some women may become lazy and lose 
    motivation at home, so if a woman goes out to the mosque, properly covered, 
    wearing hijab and avoiding making a wanton display, for the purpose of 
    praying and listening to the people of knowledge, she will be rewarded for 
    that, because this is a good purpose. End quote. 

    Fataawa Noor ‘ala ad-Darb 
    (9/489) 

    Based on that, it is preferable in your 
    case to pray Taraweeh in the mosque, but you should go out to the mosque 
    fulfilling the conditions stipulated in sharee‘ah, of conducting yourself 
    properly, covering properly, not wearing perfume, and so on. 

    Thirdly: 

    Tahajjud is (voluntary) prayer at night. 
    Some scholars stipulated that it refers to (voluntary) prayers at night 
    after having slept. 

    Taraweeh refers to prayers at night in 
    Ramadan. 

    See also the answer to question no. 
    143240

    And Allah knows best.