Yes a diameter will ALWAYS pass through the center
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This question does not make sense. All chords are not, in fact, diameters. Actually, only chords that pass through the center of a circle are diameters.
No, not all chords of a circle pass though the center of that circle. Any cord that does pass through the center of the circle is called diameter of that circle.
No, a secant line does not pass through the center of a circle. A secant line is a line that intersects a circle in two distinct points. Only a line passing through the center of a circle is called a diameter.
A diameter of a circle must pass through the center of that circle. A cord is a line segment that has its endpoints on the circumference of a circle. It can be any line segment. If that cord also passes through the center of the circle, it is said to be a diameter of that circle. A diameter of a circle is the longest cord of the circle.