I just received an offer I'm really excited about with a proposed start date 3 weeks from now, but everything is contingent on passing the background and reference check. I have no reason to be worried about this, except maybe a slight discrepancy in my current title: I'm technically an 'Associate' at my current company (which is a super old, European conglomerate with an outdated title structure) so I put 'Associate II' on my resume to more closely align with actual level of seniority, responsibilities, and pay which resembles that of a typical 'Senior Associate' in my market. I have data/pay stubs to back this up if necessary.
So a few questions:
Is that title discrepancy something that would raise red flags and get my offer rescinded?
Is it fair for me to not put in notice at my current job until all contingencies are 100% taken care of (i.e. background check is cleared)?
If so, how do I ask HR what the status of my background check is without raising any red flags?
Finally, the offer letter that I signed included reference checks, but I haven't been asked for any references. Is that something I should bring up as well?