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All cruise lines have different age limits in terms of child fares, so your starting point is choosing a cruise line. On some lines 12 yrs others up 18, these are all based on 2 adults sharing. Some lines, children are free.
I presume you are thinking of the cruise fare. On P&O there is a reduction for children sharing the same cabin of 16 and under, sometimes (mainly outside school holidays) its 100%, i.e. they go free. There are also significant reductions for a third adult sharing a cabin, which strangely are often a bigger reduction than for a child. Each cruise seems to have different reductions so you need to look at a few. The information is on the P&O website or brochure - look for "shared stateroom reductions" at the bottom of the price list, which give you the percentage reduction for and adult/child. Having sorted out what you might want, book through a cruise specialist, like this site.
Depends entirely on which cruise line you select. For example Royal Caribbean dont do child prices just a reduction in price for 3rd or 4th person sharing a cabin, regardless of age.