1. At what age do men and women become legally responsible?
If we look into chapter 4 of the Qur'an, verse 6, it says "Put the orphans to the test, until they reach the age of marriage." That age of marriage is given in the Qur'an as indicating the age of maturity. Muslim scholars explaining this verse have given us five indications showing that someone, male or female, has reached maturity. Two things in particular relate to females, which are menstruation and gestation. The beginning of menstruation marks the age of maturity for a woman, and thereafter, she becomes totally responsible from a Shari'ah point of view. Similarly, if she conceives, she is considered a senior.
The other indications of maturity common to both genders are wet dreams, the growth of body hair and age. Some commentators have said that a person automatically reaches the age of maturity at fifteen, even if other physical signs have not appeared yet. Other scholars say that the age of seventeen is the age at which maturity begins, in the absence of the other signs, while the Hanafi school have mentioned this age as being eighteen. So we look at both natural signs, and at age. After a certain age, an individual is required to carry out all the basic duties enjoined by Shari'ah.
(64 - Social Issues 3)
2. How should one dispose of sheets of the Qur'an or papers with Qur'anic verses written on them? Is the rule different when dealing with Qur'anic verses that are translated into, for example, Turkish, Urdu?
Dealing with the second part of the question first, it is important to remember that though Arabic is the language of the Qur'an, and thus accords more respect, parchment from translations written in other languages, should be treated with equal consideration. This is because, though not exactly the Qur'an, a translation nevertheless represents the writer's utmost effort to purvey its meaning.
Parchments of the Book needing to be disposed of should be burnt. Muslim countries tend to organise the process by having "Qur'an receptacles" or "Qur'anic Bin" dotted around various parts of cities and villages in prominent places. Unlike traditional refuse bins, the contents of these receptacles are not tipped into refuse trucks, together with rotting food and waste, they are taken away for burning.
In the absence of such a meticulous system of disposal, you're probably asking what should one do? I personally keep an old envelope used to collect parchments so that they should not, at any point in the process, come into contact with other waste. The paper should be washed with water only, until the ink of the words is no longer visible.
(42 - Qur'an 3)