1) It is permissible for a person to send zakaat al-fitr to another country in the case of need, such as if he does not know any poor people in the place where he is. It is permissible to delegate a trustworthy person to buy it and give it on his behalf. The Sunnah is to give it as one is going to the Eid prayer. He can find out where the poor person's house is ahead of time so that he can give it to him at the right time.
2) Allah has honored us in Ramadan by chaining up the devils, opening the gates of Paradise, closing the gates of Hell, and multiplying the reward. Fasting will intercede for a person and protect him from Hell, and admit him to Paradise through the gate of al-Rayyan.
3) If a person fasts in one country then travels to another country where the people started to fast before or after him, he comes under the same ruling as them because of the hadeeth: "The fast is the day when you [plural] fast, and al-Fitr is the day when you break the fast." This is true even if it means that he fasts more than 30 days. However, if it is less than 29 days, he should make up the shortfall after Eid. (From Shaykh Ibn Baaz)
4) The Sunnahs of Eid include reciting takbeer, doing ghusl, wearing nice clothes, and eating an odd numbers of dates. Take the woman out with you, even those who are menstruating, wearing proper hijab, so that they may witness goodness and the du'a of the Muslims. One should go walking via one route and then return by another route. One should give generously of permissible things to one's children.
5) Eid al-Fitr is just one day, the first day of Shawwal, on which it is haraam to faast. The common belief that Eid al-Fitr lasts for three days is merely a custom that is known among the people. It has nothing to do with any shar'i rulings. As for the second and the third days of Shawwal, it is permissible to fast these days to make up a missed Ramadan fast or as a voluntary fast.
6) It is narrrated in a saheeh hadeeth: "Fasting the month of Ramadan is equivalent to fasting ten months, and fasting six days of Shawwal is equivalent to fasting two months, so that is fasting for a year" i.e. it is like the obligatory fast in reward. The intention for the six nafil days of Shawwal should be made the night before. One may fast them consecutively or seperately.