There is nothing wrong with congratulating one another at the beginning of the month of Ramadan. There is nothing wrong with saying Ramadan Mubarak.

Virtues of Ramadan include the following: 1- Allah has made fasting this month the fourth pillar of Islam. 2- Allah revealed the Quran in this month. 3- Allah has blessed Ramadan with Laylat al-Qadr . 4- In this month, Allah opens the gates of Paradise and closes the gates of Hell. 5-Every night Allah has people whom He redeems from the Fire. 6- Fasting Ramadan is a means of expiation for the sins committed since the previous Ramadan.

These are the valid reasons for breaking the fast during Ramadan: 1- sickness, 2- traveling, 3 - pregnancy and breastfeeding, 4- senility and old age, 5- intense hunger and thirst, and 6- compulsion.

You should fast and break your fast with the people of the country where you reside, even if it differs from your country of origin. Similarly, on the Day of `Arafah, you should follow the local practice of your place of residence.

Whoever does not fast some days of Ramadan has to make up those days before the next Ramadan comes. For more, please see the detailed answer.

It is recommended for a Muslim to recite the Quran frequently during Ramadan and to strive to complete it. However, finishing the entire Quran is not obligatory—one is not sinful for failing to do so, though they will miss out on a great reward.

Singling out the first third of Ramadan to make Du`a for mercy, the second third to make Du`a for forgiveness and the last third to make Du`a for ransom from Hell is an innovation for which there is no basis in Islamic teachings.
There is also no justification for singling out these times for these Du`as, because all the days of Ramadan are equal in that regard. Rather the Muslim may make Du`a for whatever he wants of goodness in this world and the hereafter throughout Ramadan; that includes asking Allah for mercy, forgiveness, ransom from the Fire and admission to Paradise.

Tarawih prayer is not compulsory for women, and it is still better for them to perform the Night Prayer at home. But the fact that praying at home is preferable does not mean that women are not permitted to go to the mosque.

The one who prays eleven rak’ahs is doing well and is following the Sunnah. Whoever makes the recitation shorter and increases the number of rak’ahs is also doing well. For more, please see the detailed answer.

Taraweeh prayer is a recommended Sunnah and comes under the heading of qiyam al-layl. Whoever prays Tarawih in Ramadan out of faith and in the hope of reward, his previous sins will be forgiven.

Some Sunnahs of fasting:
1- If someone reviles you, respond to him by saying ‘I am fasting.’
2- Eating Suhur.
3- Hastening to break the fast and delaying Suhur.
4- Breaking the fast with fresh dates.
5- Saying this du`a when breaking your fast: ‘Dhahaba al-zama-u wa abtalat al-‘uruqu wa thabata al-ajr in sha Allah.’
6- Offering a lot of du`a.