PhD job process
If you are a PhD student you probably shouldn't be needing a recruiter. You should have networked during your doctoral work with people in your field and have connections (from conferences, collaboration, research, etc).
Many recruiters are not going to have the bandwidth to fit highly specialized PhD graduates to the perfect job, which might not be easily available.
Blindly sending out "ready for a job!" messages to recruiters who are not intimately familiar with your field? Probably going to result in nothing successful.
Try finding recruiters who specialize in your field (your profile suggests analytical chemistry). A quick google search suggests there are analytical chemistry recruitment agencies worldwide. Start with them. Figure out which are actually relevant and reach out to them.
If you don't have a Linked-In profile, try this. Many recruiters like this.
Your specific questions
Questions regarding the strict-ness of their qualification requirements
Recruiters don't care about this, the company they recruit for does. So this sort of question doesn't really make sense.
Questions regarding their willingness to hire a candidate with great soft skills but deficient in tech skills (and to train a candidate in certain technical skills after hiring).
This is a bad question. "I'm not qualified, but will you help me be qualified?"
General questions regarding what recruiters in their company's field look for in a candidate.
What to do instead
I think you have an overly optimistic view of what most recruiters are.
Most recruiters are paid to get people placed in positions. This is especially true of those who are not employed by the company posting the job. Companies pay them a commission of sorts (perhaps 30% of your yearly salary) when a recruiter finds them a job. Keep this in mind as you message them.
Some recruiters will be employed by the company posting the job. Their goals are similar, though they may be paid differently.
Regardless, recruiters are not paid to mentor/coach/train people, except as it furthers their goals - getting people hired. You might find a great recruiter willing to help mentor you but this is really unlikely. They interact with hundreds of people, they can't take the time to do that level of personal interaction.
Also remember that for every legitimate person that talks to them very likely dozens or even hundreds of people who are not good fits are taking their time.
Try something like:
- "Hello, I am going to be graduating in December 2015 with a PhD in Analytical Chemistry, focusing on X. I am looking for full-time employment in [locations] and am wondering if you have any openings which might fit my interests."
Basically, remember the recruiter doesn't care about your interests, they care about placing people.
Giving them the information to help you get placed is what you need to do - not get life/career advice. This is true regardless of whether they are employed by the company or not.
You want to make it easy for them to identify "does Zeejet fit any of our jobs?" - asking a bunch of related questions doesn't really help you with this. I would suggest if you want that sort of input, to seek either your industry partners or academics who previously worked in industry. Or even reaching out to technical people at the firms you want to work for - I've had surprisingly good luck sending linked-in messages blindly to people, if you approach it like:
- "Hey, I see you work for X. I am really interested in learning more about X - my background is Y, it looks like you have a similar background. Would you be willing to answer a few questions from your experience I have about working for X? I'd love to learn from you!"
It's not a 100% success rate, but flattery goes a long ways. You might have more luck this way than approaching recruiters directly.