Question 1 -- Book of Mormon witnesses
Far and away the most common reason given, as demonstrated by the 8 (currently) existing answers to this question, is that the testimony of the Book of Mormon witnesses is rejected because of what follows from it.
We can represent this approach via the logical proposition:
- P => Q (if P then Q)
- If the BoM witnesses are truthful then a variety of implications
follow (for the book, for the teachings of the faith that upholds it,
The approach taken then, is to reject P by rejecting Q. If we add a second premise, we get an argument like this:
P1: P => Q
The proof is in the pudding: this approach is used by all 8 answers that preceded this one.
Note that only 1 of the aforementioned 8 answers endeavored to directly impeach the character of the witnesses themselves--this is not surprising, as none of the 11 ever denied the claims to which he signed his name in The Testimony of the Three Witnesses & The Testimony of the Eight Witnesses, even after multiple subsequent printings of the Book of Mormon text.
Conclusion: the testimony of the witnesses is generally rejected because it carries implications which conflict with people's existing beliefs. This approach to rejecting the witnesses does not directly engage with the arguments of Book of Mormon apologists.
Question 2 - The witness of the first-century apostles
Judas Iscariot is typically not used a character witness for Christ, but the other 11 are (plus Matthias, James the Lord's brother, Barnabas, and Paul). There are 3 common reasons given to support their credibility:
1. Their fruits
If the apostles did not sincerely believe their story, the meteoric rise of the Christian faith--in spite of intense opposition--is very difficult to explain.
Note that although a similar argument is sometimes used with respect to Islam, the early, meteoric growth of each religion occurred under very different circumstances.
2. Their willingness to die
There are 4 men, named as apostles in the New Testament, for whom we have first century attestation of their death as martyrs (others probably died as martyrs, but we lack early sources for this history):
- James the son of Zebedee (Acts 12:1-2)
- James the son of Joseph (Josephus, Antiquities 20.9.1)
- Peter (1 Clement 5)
- Paul (1 Clement 5)
It would be one thing to say they died for a fraud they had been misled to believe, but quite another to say they died for a fraud they knew was false. These men were in a position to know the truth (or falsehood) of what they said.
The New Testament, 1 Clement, and other early Christian writings also describe numerous additional persecutions & sufferings (not all the way to death) endured by first-generation Christians and their leaders.
3. The witness of the Holy Spirit
This appears to be the most widespread and enduring reason given for trusting the apostles: their words, preserved in the New Testament, have been ratified by the Holy Spirit in the hearts & minds of millions (if not billions).
Most Christians have probably never read 1 Clement chapter 5 (cited above); yet they believe the words of Peter & Paul based on their own personal experience engaging with the Divine.
Paul himself would doubtless be pleased:
4 And my speech and my preaching was not with enticing words of man’s
wisdom, but in demonstration of the Spirit and of power (1 Cor. 2:4)
Conclusion: the apostles' testimony is corroborated by historical records and the living, abiding voice of Divine inspiration.