1) Welcome to the Party!
2) As you are obviously new here, I have some suggestions to help us all help you:
When you post, please post your entire configuration including (but not limited to) your installation method (7.X.X?) and vicidial version with build (VERSION: 2.X-XXXx ... BUILD: #####-####).
This IS a requirement for posting along with reading the stickies (at the top of each forum) and the manager's manual (available on EFLO.net, both free and paid versions)
You should also post: Asterisk version, telephony hardware (model number is helpful here), cluster information if you have one, and whether any other software is installed in the box. If your installation method is "manual/from scratch" you must post your operating system with version (and the .iso version from which you installed your original operating system) plus a link to the installation instructions you used. If your installation is "Hosted" list the site name of the host.
If this is a "Cloud" or "Virtual" server, please note the technology involved along with the version of that techology (ie: VMware Server Version 2.0.2). If it is not, merely stating the Motherboard model # and CPU would be helpful.
Similar to This:
Vicibox X.X from .iso | Vicidial X.X.X-XXX Build XXXXXX-XXXX | Asterisk X.X.X | Single Server | No Digium/Sangoma Hardware | No Extra Software After Installation | Intel DG35EC | Core2Quad Q6600
3) I'm not sure I follow your problem. Is it that you don't like the fact that the call (while in the IVR/Call Menu) shows as an Ingroup even though it's not in that ingroup? If so, perhaps you could make a "placeholder" ingroup with the same name as the Call Menu so the name would appear. If that's not the problem ... I'd like to hear it.
Why tracking IVR did not work without assigned group?
4) Vicidial is a massive package which has been painstakingly created by The Vicidial Group to the specifications of paying clients. If you want a feature to be added or altered, you can contact them directly and they will provide pricing and will add your required feature accordingly.
What I'm saying is: "Because nobody has paid for this yet!"
5) PoundTeam Incorporated (My employer) is also capable of this. However: Upon completion we would have to submit it to the Vicidial Issue Tracker and request inclusion rather than the Vicidial Group ... which owns this product and can add anything they deem worthy. I'd say tracking Call Menu calls in the same way as Inbound is worthy, of course, but the cleanliness of the code always comes into play when The Vicidial Group accepts a feature from someone else. That being said, we've provide similar content for others such as tracking 3-way calls after the agent has left the conference, and showing the List on the real time instead of the Ingroup.