Quitting a Job Dos and Donts

HRSB

I have read multiple websites on the dos and donts of quitting a job but all just explain how to quit gracefully and not the follow-through process. I was hoping to get some advice on the following questions:

1)    At the time of the exit interview or at the time of counter offer, should I disclose my new employer’s name? I know common sense says do not disclose your new employer but especially from a counter offer perspective my ex-employer wants to know if a similar company is offering this position or a bigger player. They claim this information helps them understand where their competition is going. I disclosed the name of the company to my manager so that he understands the frustration and reason on why I am leaving since other competing companies are giving much more than what they are offering.

2)    What are the negatives that can happen if the ex-employer knows the new company’s name?

3)    Can the new company withdraw the offer of hiring me even after the forms and job offer letter have been signed and submitted?

4)   When do I update my Linkedin profile to show my new position and company?

Something bizarre happened yesterday; the recruiter from the new company called me and said he is trying to hire a few more colleagues of mine from the old company and that he might see my old company blaming me for getting them over to the new company.

Questions that this raises in my mind:

1) Why would he call and advise me on something that is not true because I have not told anyone rests alone persuade anyone to join the new company? I am not getting any referral bonus or anything.

2) What is the power of a recruiter in a company?

3) Can a recruiter influence the joining or firing of a candidate?

4) Does the recruiter get in trouble if my ex-employer knows my new employer?

Without making this a newspaper lengthy post, I would really appreciate if someone finds it in their hearts to explain how things work on the HR side. I just want to work and do what is best for everyone involved, hopefully I do not get screwed over

Thanks