All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and messenger.
This Hadeeth was reported by Ahmad in Al-Musnad and by Al-Haakim. The latter said that it is Saheeh (sound) according to the conditions of Muslim, and Ath-Thahabi agreed with him. Shaykh Al-Albaani said: "This Hadeeth is as they both said as long as there is no discontinuity between ‘Abdullaah ibn Shaqeeq and Mihjan [two narrators of the Hadeeth], as Rajaa’ ibn Abi Rajaa’ Al-Baahili comes between them in the versions of Ahmad and Hanbal. This chain of narrators is more correct than the chain of narrators in the former version, but it (the former) is acceptable as a corroborating report (transmitted through a different chain of narrators) at any rate."
Al-Haythami said in Mujama’ Az-Zawaa'id: “It was narrated by Ahmad and its men are those of the Saheeh Hadeeth (they conform to the criteria of the narrators of a Saheeh Hadeeth).”
In the Hadeeth, it is clear that what is meant by the palace is the mosque of the Prophet (in Madeenah). This indicates the greatness of its edifice at that time. Now, it is a great edifice, if seen from a distance, it appears to be a palace.
As for your second question, we have not come across anything in the Quran, Hadeeth texts or scholarly works that indicates that the Dajjaal (Anti-Christ) has a palace in that region, let alone the palace that you refer to in the question.
Allaah Knows best.