1. If an image is SMALLER than the object is the transformation still called an enlargement?

Yes, and the scale factor will be a fraction between -1 and +1.

2. Is it possible to have an image that is smaller than the object under an enlargement?

Yes, when the scale factor is less than 1 AND greater than -1.
e.g 0.5 or -0.5

3. How many points are invariant (do not move) under an enlargement?

There is only one invariant point under an enlargement. That is the centre of enlargement.

4. How is the centre of enlargement found?

Join each object point to the corresponding image point. Where all of these lines intersect is the centre of rotation.

5. Can the scale factor for an enlargement be negative ?

Yes, this gives an upside-down image which is on the opposite side of the centre of enlargement. You will study this later.