Hey there,
I did this all the time while working at McKinsey. It is a quick way to help people, without investing a lot of effort on the consultant's side. What has been written here so far is incorrect.
This means
1. It is NOT a referral. Local HR will give input on your resume and evaluate your chances to actually get an invitation to the interviews should you decide to apply. This is a risk-free process. You might receive feedback such as: ''The academics are good but you need to go through one more internship with a prestigious industry company,...'' Use this feedback to work on your resume until you decide to apply. It might also very well be that everything is fine and you will hear that with the current resume in the current situation you will have a good chance to move through the actual screening process (this is not a guarantee either).
2. No, since it is not a referral and not an application. See above.
3. Usually HR is very quick to deliver feedback. They need a minute or 2 to gauge your resume and potential. The bottleneck might rather be the AP forwarding their message to you or adjusting their feedback :-)
Cheers
Florian