Crossing the International Dateline

What are the ramifications of crossing the international dateline for... 1. Counting the Omer when the dateline was crossed between Pesach and Shavuot? 2. Day for observing Shabbat (the 7th day after one’s last Shabbat or the day on which Shabbat is being observed in the new location)? 3. Day on which Shavuot should be celebrated when the dateline was crossed during Sfirat Haomer (50th day after Pesach or the day on which Shavuot is being observed in the new location)? 4. Day on which Shmini Atzeret should be celebrated when the dateline was crossed during Chol Hamoed (8th day after Succot or the day on which Shmini Atseret is being observed in the new location)? (and the same for the last day of Pesach)?

Shabbat and festival dates are determined by local dating, irrespective of the point of departure of the traveler. This includes the final days of Pesach and Sukkot. However, with regards to Shavuot there is an opinion that one must count the 49 days of Sfirat Haomer and then celebrate Shavuot on the 50th day, regardless of local custom, but that is a minority opinion. In regards to Sfirat Haomer ther is a dispute. For instance, if one is travelling from California to India on the morning of the 25th day, one will "move" into the 26th day when crossing the line. There is now a question whether to immediately count day 26, then continue day 27 that night (this seems to be the majority opinion), or to count day 26 that night. There are many variations of this problem that require the attention of a personal Posek. I have been told that Australians refrain from flying to California on Saturday night, lest they "fly into Shabbat". Bon voyage!