There is no contradiction. There are two different kinds of evidence being spoken of. Internally, the Holy Spirit bears witness that the Christian is a true child of God (Romans 8). Externally, there is the witness of history, archaeology, and the changed lives of millions of people from sinners to saints to show that Christianity is true.
Even the most preposterous "isms" have true believers.
Exactly. That is why faith must be evaluated. The false must be exposed.
As for prayers being answered, are you willing to assert that the "answer" to any given prayer can be known in advance, or do the answers only become known in retrospect?
Answers to prayer are regularly experienced by those who know the One True Living God.