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It is a polynomial if the square root is in a coefficient but not if it is applied to the variable. A polynomial can have only integer powers of the variable. Thus: sqrt(2)*x3 + 4*x + 3 is a polynomial expression but 2*x3 + 4*sqrt(x) + 3 is not.
1 2 3 and 4 are 4 numbers, they are not functions of any sort - cubic polynomial or otherwise.
23x + 16 are terms. This would only be an equation If there was an equal sign.
The degree of a polynomial refers to the largest exponent in the function for that polynomial. A degree 3 polynomial will have 3 as the largest exponent, but may also have smaller exponents. Both x^3 and x^3-x²+x-1 are degree three polynomials since the largest exponent is 4. The polynomial x^4+x^3 would not be degree three however because even though there is an exponent of 3, there is a higher exponent also present (in this case, 4).