1. the parent of the group does not link to any page even though it highlights as if it should. There is an option to 'hide the link' but I don't understand what this refers to as there is no link.
That option is intended for normal menu items, but unfortunately there's currently no way to hide irrelevant options when the menu item is first created. I don't believe groups are intended to work as more than an organizational item, but I'll have to check with the other developers to see if that's intended, or something that we'll need to change.
2. When you first create a group (or any) menu there is a subtext box in which you can write some description. However, once the menu is saved and you go back in to edit the subtext box is no longer visible.
When a menu item is first created, the menu editor has no way of knowing what it is, so all options show, even if they're not relevant to the item type. I'll have to do some research into ways to improve the way the menu works in the editor, but that will most likely require a massive overhaul of the code, if not a complete rewrite, so I can't even begin to guess how long it will be before an update to the menu system is available.
3. I am not sure of the function of the 'menu item type' option within the menu box. I have gotten the widget menu to work by adding 'widget' and the 'display a widget area' option but for the group option it does not change anything. For example, I tried creating a menu link to the parent page I wanted and then selecting 'group' in the menu item type. I hoped that that might show the children of the parent menu link as group children but they just appear in the normal slide out way and not grouped underneath.
Setting an existing menu item to be a group should definitely treat sub-items as group children. If it's not working that way, then it is most likely a problem in the menu code. Like with the previous question, that's probably going to require a lot of coding, so I can't even estimate how long it might take.
Thanks for being so detailed with the issues you've found. I hope my answers were helpful, and I will pass on your feedback to the other developers so we can get started on figuring out what needs to be done to improve the menu system.