1. What type of enlargement gives an image which is upside down?

With a negative scale factor. (When the image and the object are on opposite sides of the centre of enlargement.)

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 enlargement?

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

4. Is a enlargement an isometry?

No. The size and shape of the image and the object change under enlargements unless the scale factor is 1 or -1.

5. How is the centre of enlargement found?

Join two or more object points to the corresponding image points. 
Where these lines intersect is the centre of rotation.