12^3-1=1727
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There would need to be a digit which represents Ten. This would be the largest digit. Any number can be represented in any number-base system, so there is no 'largest number' just largest digit. Base eleven is not commonly used as some of the others (like hexadecimal, which uses letters A-F to represent ten through fifteen). You could use A for ten or maybe you want to use X (like roman numeral ten).
5037 = 248 = 3059
Not in a way that would be generally understood. However, it is possible. An 8-digit number in base 10 can be represented by a 5-digit number in base 32. For example, extending the scheme for labeling digits for base 32, VVVVV32 = 3355443110 Similarly, the 8-digit number 33333333 in base 4 is the 5-digit number 65535 in base 10
Perhaps we are thinking of the number 898? If so, then 8+9+8=25. But I am confused by the use of the plural "numbers", when there is only one largest. If I mistake the question, please rephrase it.
The decimal complement of the number 1 is 8. You can find the complement of any digit by subtracting it from the largest single digit value in the base that you're working in.