Fasting in Islam, (known as Sawm (صَوْم) or Siyām (صِيَام), also commonly known as Rūzeh or Rōzah (Persian: روزه)), is the practice of abstaining, usually from food, drink, smoking, and sexual activity. During the Islamic holy month of Ramadan Sawm is observed between dawn and sunset when the evening adhan is sounded.
You must do Qadha and also do the Kaffara of deliberately breaking the fast which is either fasting two months continuously or feeding sixty poor believers for every day of broken fast. You also need to seek forgiveness for that sin.
After being sure that all your obligatory fasting days are done, it recommended to fast on every Monday and every Thursday, or first Thursday and last Thursday and Middle Wednesday in every lunar month.
Taharah is a real condition شرط واقعي in Prayers and fasting. Any worship which requires Purity (Taharah) is invalid if it was done with out purity.
If you could not learn basic rules of Ghusl and never been informed that Ghusl is obligatory in certain cases, which is very rare now a days, then the rule is different. But if you knew about Ghusl and it becomes obligatory in certain situations, and you did not know that it applies on you, and you fasted with out Ghusl, then you need to perform the obligatory Ghusl then perform every worship which was performed with out Ghusl.
You can read the verdict of Ayatullah Sustani as follows:
Ruling 1593. If a junub in the month of Ramadan forgets to perform ghusl and remembers after one day, he must keep a qaḍāʾ fast for that day; and if he remembers after a few days, he must keep a qaḍāʾ fast for all the days that he is certain to have been junub on. For example, if he does not know whether he was junub for three or four days, he must keep qaḍāʾ fasts for three days.
If you did not know, and you did not have the ability to educate yourself about these things, then your fasting is valid. Otherwise, you will need to do qadha.
ِAnd Allah knows best
If you deliberately broke any the fast of any day of the month of Ramadan, you need to pay Kaffara beside Qaza and Istighfaar. Kaffara for every day of broken or deliberately missed fast is feeding sixty poor believers. Feeding means giving them one meal of food or at least 750 grams of wheat or rice or any food item.
If broke the fast with out knowing that it is obligatory on you to fast, then just Qaza of the fast is enough.
If you did that thinking that Fajr time did not come yet, your fasting is valid.
Yes it is recommended to fast on A'rafat day for those who are not traveling and don't become weak to perform the recommended A'maal of A'rafah.
Pilgrims in A'rafat don't fast because they are travelers.
Recommended fast can be broken any time. It is recommended to eat or drink if a Mo'min invite you while your fasting a recommended fast with out telling him that you are fasting.
No need for permission of parents in recommended fast nor in other recommended worship.
You do not need to pay a kaffarah.
All you must do is redo that day as qadha`.
And Allah knows best.
It does not break the fast no matter how bad it is. Fast breaks only in commuting any of the nine Mufattiraat ( fasting invalidating acts)e.g. Eating, drinking, smoking, lying on Allah or on The Infallible etc.
Many sinful acts do not invalidate fast despite the fact that they are sinful.
Yes, it is valid, and it would not affect the fasting.
And Allah knows best.
Yes it is permissible to cut nails and hair while fasting.