Are the manifestations truly one person? Or do they just live with the same spirit from God? If they are one person, as Bahai literature sometimes seems to suggest, how does this work? Is it some form of specialized reincarnation?
Chapters 38 and 39 of Some Answered Questions by 'Abdu'l-Bahá touch upon the fact that the Manifestations have their own individualities as well as sharing in the common inspiration of the Holy Spirit. However, there are, as you mention, quite a few references to the mystic unity of the Prophets and chosen ones of God, but this does not necessarily mean in identity. Bahá'u'lláh explains in His "Book of Certitude", the Kitáb-i-Íqán, that references in the Scriptures to Return refer to the essence of the being (i.e., the same qualities returning) rather than to individual identities.
How do members of the Bahai faith deal with the documented evidence suggesting that the Bab believed the next manifestation would not arrive anywhere near as soon as Bahaullah did? How do you deal with the evidence that he appointed a leader who seems to have been Bahaullah's older, half-brother?
I'm not sure what you're referring to, but there are several prophecies of the Báb alluding to (if not outright mentioning) both the name and date of Bahá'u'lláh's coming.
The following passage from "God Passes By", by Shoghi Effendi, the Guardian of the Bahá'í Faith, and great-grand-son of Bahá'u'lláh, answers both of these questions:
Some of His disciples the Báb assiduously prepared to expect the imminent Revelation. Others He orally assured would live to see its day. To Mullá Báqir, one of the Letters of the Living, He actually prophesied, in a Tablet addressed to him, that he would meet the Promised One face to face. To Sáyyah, another disciple, He gave verbally a similar assurance. Mullá Husayn He directed to Tihrán, assuring him that in that city was enshrined a Mystery Whose light neither Hijáz nor Shíráz could rival. Quddús, on the eve of his final separation from Him, was promised that he would attain the presence of the One Who was the sole Object of their adoration and love. To Shaykh Hasan-i-Zunúzí He declared while in Máh-Ku that he would behold in Kárbilá the countenance of the promised Husayn. On Dayyán He conferred the title of "the third Letter to believe in Him Whom God shall make manifest," while to Azím He divulged, in the Kitáb-i-Panj-Sha'n, the name, and announced the approaching advent, of Him Who was to consummate His own Revelation.
A successor or vicegerent the Báb never named, an interpreter of His teachings He refrained from appointing. So transparently clear were His references to the Promised One, so brief was to be the duration of His own Dispensation, that neither the one nor the other was deemed necessary. All He did was, according to the testimony of `Abdu'l-Bahá in "A Traveller's Narrative," to nominate, on the advice of Bahá'u'lláh and of another disciple, Mírzá Yahyá, who would act solely as a figure-head pending the manifestation of the Promised One, thus enabling Bahá'u'lláh to promote, in relative security, the Cause so dear to His heart.
Why was there such a short time between these two manifestations when the average timespan had been about 500 years prior to this?
This is explained in our Writings as being both a great mystery, as well as testifying to the potency of this Age, in that, although Their Dispensations are separate and independent (unlike that of John the Baptist's preparation of the people for Jesus), the Báb and Bahá'u'lláh can also be considered the Twin Manifestations of God for this Day and thus Their coming has infused this Day with a very special potency. Many of Bahá'u'lláh's Teachings refer to the Báb, and it was the purpose of the Báb, as He stated, to exalt and magnify the Cause of Bahá'u'lláh in preparation for His immanent coming.
I'll try to answer your last questions later.