Currently, Prince Harry is third in the line of succession to the British throne, behind his father Prince Charles and his older brother Prince William.
Prince Harry
Prince Henry of Wales (Harry).
Prince William will get the throne, since he is older and therefore has a higher place in the line of succession.
Prince Harry is a newly promoted Captain in the Household Cavalry's Blues and Royals.
They are brothers - both are children of Charles, Prince of Wales and the late Lady Diana (former Princess of Wales). As of July 2017, Prince William stands 2nd in order of succession to the British throne (behind his father, Prince Charles) while Prince Harry is 5th. (Williams kids are ahead of Harry in the line of succession.)
Harry has not given up his right to the throne, he is currently fifth in the line of succession.
His eldest son, William. Prince Harry his 2nd son is 3rd in line to the throne.
Prince Charles is next in line. Behind him is his eldest son Prince William. If Prince William ever has children, his eldest would be next in line. If Prince William never has children, then his brother Prince Harry would be next in line.
If you're talking about the line of succession, then if Prince William became king, but died without fathering an heir, then his brother Harry is the next in line for the throne.
Prince Harry is not married
The British Royal Family is Church of England, with Queen Elizabeth II being the "Supreme Governor of the Church of England". Catholics, or anyone who marries a Catholic, cannot be in line for succession to the throne. Prince Harry most definitely does not have to marry a Catholic.
Prince Harry