Reading Quran and it's transliteration in English or any other language and Arabic during menstrual period is permissible as far as you don't read the four verses of obligatory Sajda ( in Suras Al-'Alaq, Al-Najm, Al-Sajda and Fussilat).
Touching the book is allowed but touching the text of Quranic words and its translation is not permissible not only during menstrual period but also for any one who is with out a valid Wudhu.
There are several surviving recitations (qira'at) of the Qur'an with very minor differences (mostly related to pronunciation such as a vowel sound or dots). Most of them are unused.
The differences typically have little impact on the meaning, although may be considered in jurisprudence or tafsir.
This is not considered to be tahrif (alteration) of the Qur'an, especially since it is nearly inconsequential.
In Sunni hadith, the Qur'an is said to have been revealed in seven dialects (ahruf).
The Shi'i view is that there is only one original correct revelation and recitation, even if, in reality, there exist multiple qira'at.
There are many online learning Arabic courses. Some of them are free while others are paid. There are also Application for learning Arabic which be obtained from App Store and other sites. You can search and select a suitable course for you. I can not suggest a specific course for you because it depends on your level in Arabic language and in your time and task in learning Arabic.
Obviously, learning any language needs practicing, so, try to practice whatever little you learn so that you will be more able to learn more.
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