Hi noseman, I'm glad you're getting some use out of MoI now! :)

So for showing points - when you have a "B-rep" type model structure like MoI does for its solids, you can't generally show points on things like boundary edges because trying to move them around would open up gaps between areas that are supposed to have a shared edge.

There is some description of this here:
http://moi3d.com/faq#Q:_Why_does_show_points_work_for_some_objects_but_not_others.3F

But to answer your question about how to get rid of the edges being split up into pieces, (EDIT: I see Pilou already answered!) there is a hidden "Merge" command that you can use for that purpose:
https://moi3d.com/4.0/docs/moi_command_reference10.htm#merge

So your first step of deleting the top is correct. Then select the edges that are fragmented, press the Tab key (keyboard focus will go into the X/Y/Z input in the bottom toolbar), then type Merge and push Enter. That should glue the fragments into a longer single edge.

I don't like having the Merge command hidden like that but I've also been trying to avoid having both "Join" and "Merge" separate buttons next to each other because they're just too close in meaning. So I've been planning on reworking the Join command so that it would be able to do both of those functions with some options in it. I haven't had a chance to get to that yet (it will probably involve some new UI concepts to be designed which is a very slow and methodical process for MoI) but I would like to get to that pretty soon.

Then after you've done that and you want to fill in that hole a quick way to do it is select the entire object and then use Construct > Planar, it will build a surface where there are planar openings and also automatically join it.

- Michael