Hi Guy, is it possible for you to post the 3DM model file of your object there instead of just a screenshot?
It usually helps quite a lot to be able to deal with the actual geometry that your question involves, because I'm able to do a lot of things to geometry such as rotate it to different angles, zoom in to it, and also just use your actual file to demonstrate things with, none of these things are possible for me to do on just a screenshot instead of the actual model.
#1 looks like it's just likely to be a display artifact - in order to display the shaded surface area, MoI has to convert surfaces into a triangle mesh and in some situations where your surface has fairly shallow or gentle curvature it can get not quite enough triangles created for the display in those areas, leaving a kind of polygonal silhouette to the shaded drawing.
That kind of thing is purely a display artifact, it does not mean that your actual surfaces are that way, and if you for example export to a polygon mesh format using a high density for the export you should see that area getting refined during the export.
Curves are drawn to a higher precision than the shaded surface areas - curves get broken down into lines dynamically so that the lines used for the display are within 1 pixel of the true curve. It's unfortunately too calculation intensive to do the same dynamic refinement for surfaces so surfaces only get one static triangulation which is used at all zoom levels, so that's why there can be some mismatch between the shaded surface display and the edge display.
Some previous discussion here:
http://moi3d.com/forum/index.php?webtag=MOI&msg=4926.25
http://moi3d.com/forum/index.php?webtag=MOI&msg=4860.1
In general it's a focus for the display mechanism to do things fast and also to do things within the constraints of how the video card is set up to operate, so it's not unusual for there to be various kinds of display artifacts since trying to do a perfect looking display like an "offline render" does is much slower.
> 2) How can I make a surface covering this half empty circle ?
Are you sure it's empty? It kind of looks like it already has a surface there, if you can post the model file I can more easily check it.
If it is empty and it's a planar opening you can seal that off by selecting the object and using Construct > Planar.
> 3) how can I erase this edge to obtain a smooth unique surface here ?
Those are 2 smaller surfaces coming together at that common edge - in order to not have an edge there you would instead need to create a larger extended surface that went across that full area and that larger surface could then be trimmed to have the inner notch hole area cut out of it.
Often times if you want smooth pieces it's best for the smooth piece to be made up of one larger surface (done with one large sweep or network or whatever), and then that large single surface can get cut where necessary to remove portions of it.
Also depending on your shape there it might have been better to have made that whole surface done more as a boolean operation slicing away material from a larger block, I'm not entirely sure since I am not able to examine your model yet but it looks like you may be modeling things in a sort of more "patch by patch" method rather than building larger extended blocks and then slicing the big block up.
Generally if you can build extended pieces which then get cut it's a better workflow than trying to build things one little patch fragment at a time.
- Michael