What evidence exists to support church traditions regarding the deaths of the following apostles? The Bible tells us that King Herod had James killed by the sword (Acts 12:2) but says nothing about the death of Peter, although Jesus made reference to his martyrdom (John 21:18).  Is there any evidence to support the tradition that Peter was crucified upside-down in Rome?

The most commonly accepted tradition regarding the death of Paul comes from the writings of Eusebius, an early church historian.  Eusebius claimed that Paul was beheaded at the order of the Roman emperor Nero or one of his subordinates.   Because Paul was a Roman citizen (Acts 22:28), he was not crucified.  Is there a reliable source of information to confirm how Paul died?

Although John died peacefully as an old man, there is a tradition that he was boiled in a basin of boiling oil during a wave of persecution in Rome, but miraculously survived.  He died in Turkey.  Are there any records that support this account of being boiled in oil?

Andrew was severely whipped then crucified on an x-shaped cross in Greece, taking two days to die. Is there any record of this event?

Church tradition says that Thomas travelled by sea to India in AD 52. He was later martyred and buried there after witnessing to the Indian people.  Is there any historical evidence about this?
I suspect that Eusebius of Caesarea (c. 260–c. 340) might be the best source of reliable information given his prolific works on church history.


  In his Church History or Ecclesiastical History, Eusebius wrote the first surviving history of the Christian Church as a chronologically-ordered account, based on earlier sources, complete from the period of the Apostles to his own epoch.[49] The time scheme correlated the history with the reigns of the Roman Emperors, and the scope was broad. Included were the bishops and other teachers of the Church, Christian relations with the Jews and those deemed heretical, and the Christian martyrs through 324.[50] Although its accuracy and biases have been questioned,[51] it remains an important source on the early church due to Eusebius's access to materials now lost.[52]  


Sources:   

Eusebius of Caesarea  

Church History (Eusebius)

However, I simply don’t know where to start!  Any links to reliable sources would be appreciated.  What evidence exists to support church traditions on the persecution and martyrdom of Peter, John, Andrew, Thomas and Paul?
Foxe's Book of Martyrs used to be considered a standard textbook on the matter, but whether it is still considered so to be, I wouldn't know. It is certainly an excellent source. 

It is said (I don't know how true it is) that in England (I assume this refers to the seventeenth century, or so) there were fireplaces in homes that had two niches in them, one each side of the fire.

One niche was for the Authorised Version of the Bible and the other niche was for Foxe's Book of Martyrs.