MapPoint can draw simple lines from one point to another. Technically these are segments of a Great Circle. As the shortest line on the Earth’s surface, long lines may appear curved when zoomed out a long way due to the map projection.
Simple lines are drawn using the Line and Arrow buttons on the Drawing toolbar:
The Drawing Toolbar
To draw a line, click on the Line button. Then click on the map at the desired start point, and drag the mouse to the required end point. Release the mouse button at the required end point.
Arrows are drawn in the same way, but an arrow head is drawn at the line’s end. Here are a couple of examples:

Sample MapPoint lines including an arrow
The arrow heads of all lines, arrows, and freeform shapes can be changed. Do this by selecting the shape and then pressing the “Arrows” button on the far right of the Drawing Toolbar. This has a drop down where you can select between no arrows, an arrow at the start, an arrow at the end, or arrows at both ends:

Selecting arrows for a MapPoint line

Is there a way to combine several lines I have drawn into one “object” then copy that to another map?
Not as such. Our MPSuperShape product can be used to copy shapes between maps by exporting/importing them, although depending on your application it might be a bit cumbersome for this. Joining open lines would require custom programming.