Does Christianity give a reason for life experiences, such as in Hinduism? In Hinduism, there is a concept of past life karma. 

Meaning if someone is born into an unfortunate situation (in a slum, for example) it is because they are paying for sin from a past life.

Does Christianity or the Bible give any insight into why it seems like some people are here on vacation and others full of strife and sorrow (and everything in between)?

Also, did Jesus specifically address this (or did any of His disciples ask about this)?
It might be nice to believe that anyone who suffers must deserve it because of some evil thing he did, that everyone always gets exactly what he deserves, good or bad. But Christianity does not teach that.

As Asfallows and Thomas point out, in John 9 Jesus was specifically asked if a particular case of suffering was punishment for a person's sin, and he specifically said no.

This is not to say that suffering is never the result of sin. It often is. For example, Matthew 26:52 


  "But Jesus said to him, 'Put your sword in its place, for all who take
  the sword will perish by the sword.'"


The Old Testament contains many warnings on the consequences of sin. Like Proberbs 10:27-29 "The fear of the Lord prolongs days, But the years of the wicked will be shortened. The hope of the righteous will be gladness,
But the expectation of the wicked will perish. he way of the Lord is strength for the upright, But destruction will come to the workers of iniquity."

Many people have the idea that the Bible says that at least there will be justice in eternity, that good people will be rewarded in Heaven and bad people will be punished in Hell. But again, this is not what the Bible says at all. 

Ephesians 2:8-9 


  "For by grace you have been saved through faith, and that not of
  yourselves; it is the gift of God, not of works, lest anyone should
  boast."


Heaven is not a reward for good works, but is a gift that God freely gives to all who ask for it and accept Jesus Christ as savior. According to the Bible, people who have committed all sorts of sins will be forgiven for the asking: David was guilty of adultery and murder, Rahab was a prostitute, etc. The thief on the cross was saved in the last minutes of his life. He clearly had no chance to do anything to make up for his past sins.

God is not "fair". He is merciful. He doesn't give us what we deserve. He gives us something so much better.