regarding preparation time: From my experience, once you went through the consulting application cycle once, preparation gets easier, meaning all the case basics and case solving skills can be refreshed quite easily. I would suggest:
- Take a couple of days to go through all the case theory again until you know the concepts by heart (2-3 days should be enough)
- Do a couple of cases with different interview partners (both as interviewee and interviewer) - you will notice pretty quickly where you stand (adjust the number of case meetings accordingly) and figure out how much more time you need (typically 2-3 weeks)
- Prepare the personal fit part and focus especially on what you liked about your internship at BCG and how this made you decide to start full-time (but don't forget about reasons why McK or Bain may be a better fit than BCG, if you go there)
The case part should be comparable to the internship interviews, but for the personal fit part you should be able to fully convince the interviewer that you are motivated to do this job for a couple of years instead of only a few weeks (may this candidate become partner at some point in time?).
Regarding your second question: It is always possible to ask HR whether it is possible to start in November, January or whenever you would like to do so. They should know best.
When it comes to chances of getting in however, the question is whether the office you are applying for has a specific recruiting target for the year. If so, it is obviously a bit harder to start towards the end of the year than in the beginning. However, I have never seen a consultancy who would reject a super strong candidate only because they have already met their target…
Hope this helps!