As for wiping on the socks, scholars are unanimous on the permissibility of wiping on leather socks. Although, they are divided on the permissibility of wiping on other types of socks (i.e. cotton, nylon, etc.). Authentic scholars and mujtahids like Ibn Taymiyyah have affirmed the permissibility of wiping on such socks provided the following conditions:
a) Socks or stockings must be thick and not transparent so that water does not seep through when wiped over.
b) They must cover both the lower and upper parts of the feet including the ankle bones.
c) They must be put on after making wudu’ (ablution) or ghusl (bathing), while one is still pure.
d) Taking them off does not break one’s wudu’, although one must wash the feet completely the next time he or she makes wudu’.
e) Wiping must not exceed the period of one full day and night in the case of a resident and three days and nights for a traveler.
f) Finally, one must remove the socks if ghusl (bathing) becomes obligatory.
As far as touching the Qur’an without wudu’, the four school of thoughts hold the opinion that being in the state of purity is condition for touching the Qur’an. Some contemporary scholars see it to be only highly recommended but not a condition.
Finally, praying to Allah inside the salah is of two types. The first type is the prayers that are an original part of the salah (i.e. remembrance of ruku` and sujud, tashahud, and etc). Such prayers can be said in a language other than Arabic only for those who are not able to say them in Arabic, according to Shafi`is and Hanbalis. The second type is personal prayers that one makes in the salah in sujud or after tashahud; for this type, it is only permissible in Arabic according to the majority of scholars. As for praying to Allah outside the salah, it is permissible in any language.