-7 is a square root of 49 F - No it's true.
If PQ = QR, then Q is the midpoint of segment PR. - Not necessarily, only if P, Q, R are on the same line. If PQR is an isosceles triangle it's false.
If a segment is entirely contained in S, then S is a convex set. - Not necessarily. If all line segments whose start and end points are in S are completely in S, then S is convex.
If A, B, and C are three collinear points and AB<AC, then A-B-C
- This is not a complete statement.
On the line PR the coordinate of point P is 17 and the coordinate of R is -6. Then PR = |17-6|. T
- Again this appears incomplete, I can't see how "17" and "-6" are complete definitions of co-ordinates.
A point and a line always lie in exactly one plane. F
- Actually this is true.
Two points sometimes lie in exactly one plane
- Never. There is always an infinite number of planes containing the line joining two points. At least in 3 or more dimensions.
Two intersecting lines sometimes lie in exactly one plane
- Always, at least in 3D.
A half plane never contains its edge
- Sorry, not sure whether this is true or not.
Four points, three of which are collinear, are never coplanar
- No, the answer's "always".
Not sure about the last two in your list, I'm out of practice with these geometrical definitions.