Base N To Decimal Converter
It's weird that you offer two public functions: a general-purpose convertToDecimal(), and a calculateDecimalCharacterValue() that does the same thing but with more restrictive validation.  The latter should be a private helper function.

You are over-complicating things by a lot: the whole thing could be accomplished with Integer.parseInt(s, radix).  And — not that you would need it — calculateDecimalCharacterValue(c, base) could be done using Character.digit(ch, radix).

Technically, you aren't converting to and from decimal (base ten).  You are parsing numbers in a base-N representation to an int; it just happens that ints are conventionally formatted in base ten when you do things like System.out.println().  So, the function names aren't quite right.

You shouldn't need to use Math.pow().  The usual algorithm goes like this:

public static int convertFromBase(int base, String input) {
    // Validation omitted here...

    int result = 0;
    for (char c : input.toCharArray()) {
        result = result * base + Character.digit(c, base);
    }
    return result;
}