Questions back to you are: Is McK/Consulting still the right move for you? Can you show improvements on the feedback points in the next 12-18 months?

If Yes, then I dont see why you shouldnt give it another go. So many people I know did it in 2nd attempt. Obviously, dont bet everything on this and explore other roles & firms in parallel. Maybe something of a better FIT comes along.

Have a look at this article I have recently published which will give you a lot of tips/tricks and guidance: https://www.preplounge.com/en/how-do-i-know-which-career-is-right-for-me

You always stand a chance where you clearly have a good profile. I would go back through your interviewers feedback and start preparing accordingly. It's also worth noting that the avg. times a McKinsey offeree has applied to the firm is closer to 2 than 1. In other words, many don't get to an offer at first instance and will reapply, sometimes the next year but for many a few years later after an MBA, etc.

Good luck!

Yes, it does. Depending on country there is typically a cool-off period of 12-24 months during which you can't re-apply, but after that it's a clean sheet.

Note though that from the fact that they encouraged you to re-apply you can't really infer whether that was a serious encouragement or just something they are saying to make you feel better. E.g. sometimes as an interviewers you can tell that the underperformance is simply due to a lack of preparation that can be fixed easily. In these cases I specifically ask candidates to re-apply as I think it's the firms loss to lose them. But some interviewers just tell this to everyone they give feedback to and there's no way for you to gauge this. 

Absolutely you stand a 2nd chance! Everyone does!

Now, their comments don't really mean anything (they say this regardless as to whether they want/need you to or not). However, I can't tell you how many people I've met who bombed their first interviews, went on to to 2nd interviews a year a two later and got the offer!