Part A
point.vec file here
Part B
I believe Idrisi rasterized the point vector data (point.vec) in the following way:
The point.vec ASCII file contains data about the feature ID, the number of values of that feature ID and the co-ordinates of that feature ID point (we know it's a point file shown by the one value to each ID). So, we know from the ASCII file that the x and y min/max values are 0, 5.8 and 0, 5.7 respectively. We also input these parameters when executing a File | Document with the native point.vec.
After the file is converted to a binary type, a POINTRAS function is executed, following an INITIAL function to output point.img as a backdrop to point.vec. As point.img is initialized with extents, those of which in point.vec which extend beyond those of point.img are not displayed. For example, if the co-ordinates of a point were 9 3, it would not show up when displaying point.vec on point.img.
The POINTRAS function takes in the rows, columns, x, and y values of point.img and cross references them to point.vec; where the co-ordinates of the vector file overlap with those of the image file, a match is found and the cell feature is displayed. Therefore, the POINTRAS function displays the point data and the pixel in which the point(s) reside(s). For example, point 4 resides at x-5.8, y-3.0, which results in the pixel value of x-6, y-3. As the y value is not quite 6 in the vector file, the pixel preceding the absolute 6 value is shown. The above image also indicates that for the point.vec value that are whole (3.0), the x values are rasterized to the preceding pixel, whereas the y values are rasterized to the proceeding pixel (e.g. points 4, 5, 6). Points 7 and 8 are interesting in that if one was to rasterize the point file to show values of the sum of the identifiers of points, the value of the pixel would change. Finally, adding point.vec as a layer to point.img shows the points, georeferenced.