1:
After the resurrection of the dead, will those who resurrected die again?
The Rishonim are divided on this question. According to the Rambam and Ibn Ezra those that merit resurrection will indeed die once again.
Rambam, Treatise on Resurrection:
אלו האנשים אשר ישובו נפשותם לגופות ההם, יאכלו וישתו וישגלו ויולידו
וימותו אחרי חיים ארוכים מאוד כחיים הנמצאים בימות המשיח. ואמנם החיים
שאין מוות אחריהם, הוא חיי העה"ב, אחר שאין גוף בהם. שאנחנו נאמין, והוא
האמת אצל כל בן דעת, שהעה"ב נפשות מבלי גופות כמלאכים.
Those
individuals whose souls return to their bodies [after death] will eat
and drink and engage in sexual intercourse and sire children and die
after an extremely long life like the life which will exist during the
days of the Messiah. Further, the life following which there is no
death, is the life in the world to come because there are no
[physical] bodies there. We firmly believe and this is the truth which
every intelligent person accepts that in the world to come souls
without bodies will exist like angels.
Ibn Ezra, Daniel 12:2:
שהצדיקים שמתו בגלות יחיו בבוא הגואל כי עליהם כתוב כימי העץ ימי עמי
ואז יתענגו בלויתן ובזיז ובבהמות וימותו פעם שניה ויחיו בתחית המתים
בהיותם בעולם הבא, שאינם אוכלים ושותים רק נהנים מזיו שכינה
The righteous who died in exile will be resurrected when the messiah
comes, for to them apply the words, "the days of My people shall be as
lng as the days of the tree." (Is. 65:22) They will delight themselves
with Leviathan, Ziz, and Behemoth and die a second time, only to be
resurrected again in the world-to-come, in which they will neighter
eat nor drink but instead behold and enjoy the glory of the divine
presence.
2:
If so: Why then do the dead resurrect?
The Rambam doesn't really explore or speculate on the purpose of the resurrection, but emphasizes that belief in the occurrence of this wondrous miracle is a function of belief in the words of the prophets and Hazal.
3:
And where or what is the final destination?
In the Maimonidean tradition, it is the immortal and non-corporeal life of the soul. It is this stage of existence which he refers to as 'Olam ha-Ba (the World to Come). You can find a description of his conception in Ch. 8 of Hilkhoth Teshubhah.
The Ramban (in Sha'ar ha-Gemul) disagreed with all of this and held that after one dies, the soul goes to Gan Eden and upon resurrection the soul is reunited with the body, which is then in a purified state and goes on to live eternally. It is this last stage which he refers to as 'Olam ha-Ba.