Yes.
Yes.
Yes.
Yes.
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In real-world math, there is no "largest" integer or floating point number. This is covered by the concepts known as "infinity" and "irrationality." Depending on the processor and/or application, a number with significant digits into the thousands can be operated upon.
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No, 9.6 is a floating-point number. Integers are whole numbers without fractional parts.
Basically you use a double-precision floating point number for the real part, a double-precision floating point number for the imaginary part, and write methods for any operation you want to include (such as addition, etc.; trigonometric functions, exponential function).
fixed/floating point choice is an important ISA condition.