How to network with partners before applying?

Hi, 

I’m a postdoc, preparing to apply to consulting firms as an experienced hire later this year.

I have spoken with a few consultants to learn more about their experiences, offices and recruiting timelines, but I’m less clear on how to approach more senior people, especially partners or principals, for networking conversations.

I would appreciate your advice on:

1. How should I write an effective cold email or LinkedIn message to Partners for a networking chat?
2. What are good questions to ask during a partner-level networking call?
3. How can I ask for a referral without being pushy?
4. Given how busy partners are, what usually motivates them to respond to networking requests from candidates?

Thank you!