you are correct

consider the sine function or the cosine function or the tangent function or the cotangent function or ...2. Can the graph intersect the x-axis an infinite number of times?

My question is can a function be of an infinite degree? Does this scenario make sense?

the roots include multiplicity. so it can have as many roots as its degree, or it can have less (even if all roots are real), or it can have no real roots at all.3. If the function is a polynomial, how can you predict the number of times it might cross the x-axis?

The answer that I believe is right for this is that the polynomial function will have as many roots as the number of its degree, providing that all the roots are real numbers.