I'm not clear what your ultimate objectives are or the nature of your current role.
I presume your current role is either a short-term consulting project or most likely a secondment or interim role of sorts?
Either way, it sounds like an excellent role for a new graduate to have. Not only will you gain the skills you mention, but becuase of the secondment nature of the role you will be able to differentiate yourself from your peers by having some real industry depth. Also, the brand on your CV will impress internally and externally.
1. With respect to your first question and comment regarding 'a more consutancy based role' - the work you're doing is very much in line with a typical consulting engagement. It also sounds like you have a good level of responsibility for a graduate so I wouldnt worry.
Of course, if you have no interest in persuing a career in operations or consumer business then it is less appealing. Even so, the brand, analytical nature of work and business exposure will still put you in a strong position for most other future roles in and out of consulting.
2. If this is a secondment role it's likely the optimum time to be in it is 6-9 months. Assuming the role hasn't expanded by that time then I expect you will have learnt 80% of what there is to learn and be developing at a slower rate.
If this is an interim role or you are not employed by a consulting firm who can assign you to another project, then you may want to consider staying for a year or more so as to strengthen your CV.
3. Qualifications are alwys useful, but I wouldn't consider specific 'management consulting' qualifications. Instead consider project management or accounting/finance qualifications as these are most highly regarded in consulting.
Hope that helps