Yep.

The Trapezoidal Rule is exact when integrating any linear function.

Simpson's Rule is exact when integrating any quadratic or cubic. Generally it's also more accurate with integrating any curvy function.

It shouldn't matter how many subintervals there are. Because you're just approximating the curve with trapeziums, having 5 trapeziums vs. having 6 shouldn't make a difference (aside from the increased accuracy you get with more function values).

Yes, it must be even otherwise Simpson's Rule won't work properly, since it uses three points (two subintervals) to generate the parabola that approximates the curve. So curves are always approximated two subintervals at a time.

Yep. More subintervals means your trapeziums/parabolas will better approximate the function.

Besides taking more subintervals, you can't really improve on the accuracy without changing the rule itself.

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