If an Israeli resident travels outside of Israel with the intention of staying abroad for a month or two, he retains the law of an Israeli resident who happens to be outside of Israel for the holidays; his laws have already been discussed in the previous Halacha.
Those who are sent abroad by certain organizations, such as those sent by the Jewish Agency and the like, who reside outside of Israel with their families for a temporary period of time, but all the while have in mind to return to Israel when their temporary stay is finished, since it is understood from beforehand that their stay abroad usually spans a year or two, as long as they are outside of Israel they must conduct themselves exactly like the other non-Israeli residents around them regarding the second day of Yom Tov, whether in public or in private. They must therefore recite Yom Tov prayers on the second day of Yom Tov with the other non-Israeli residents; similarly, they may not don Tefillin on the second day of Yom Tov even though it is a regular weekday for Israeli residents. Additionally, they would have to conduct a second Seder on the second night of Pesach, and regarding all laws, they are no different than any non-Israeli residents.
If a non-Israeli resident makes Aliyah (moves to Israel), however, he is uncertain if he will find a way to earn a livelihood there, for if he is successful, he will settle in Israel, and if not, he will move back to his former place outside of Israel, he must still observe two days of Yom Tov like other non-Israeli residents, for he has not yet completely mentally uprooted himself from his place outside of Israel; thus, he is considered like a non-Israeli resident staying abroad in Israel.
If a single man who is independent, meaning that he is not necessarily contingent on his parents’ wishes, moves to Israel, he observes only one day of Yom Tov similar to Israeli residents, in hopes that he will find a wife in Israel and settle there. However, if he says that he is contingent on his parents’ wishes and they have requested that he return home to outside of Israel, he must then observe two days of Yom Tov. Nevertheless, if he knows in his heart that, were an appropriate marriage prospect to arise and, financially speaking, if he would be able to settle in Israel, he would, and additionally, were these scenarios to occur, he would refuse his parents’ request to return home to outside of Israel (which is indeed Halachically permissible in this kind of situation), he should conduct himself like an Israeli resident and he need not observe a second day of Yom Tov.
If a non-Israeli resident owns an established home or apartment in Israel and spends each of the three festivals (Pesach, Shavuot, and Sukkot) in his home in Israel, he need not observe a second day of Yom Tov. Although he spends most of the year in his home outside of Israel, nevertheless, since he spends each of the festivals in Israel, he is considered an Israeli resident with regards to the holidays.
Regarding the order for the reading on the night of Shavuot, we have already discussed this matter in a special Halacha (in Hebrew) and it can be seen by clicking here: "תיקון ליל שבועות".