Last Interview and Background Check

Okay, I have my last interview with a firm this coming Monday and I have to say I'm pretty excited to get this far. But I have one dilemma.

They have attached a few documents via email to be filled out when arriving to my last interview. These documents are just employment, drug urination, and background check information that I have to sign. Easy. But the question I want to ask is how intensive are background checks in general? I was employed at a retail store my freshman year contracted to work for about 3 months. So immediately upon employment, I listed my contracted date onto my resume. However, I had to leave work about 2 weeks earlier due to school and family obligations, but failed to update it on my resume. I realized it after submitting my internship applications and am quite worried. I have heard companies do not always go through background checks as they put it there for professional reasons or will go through it if they're suspicious.

If they call my ex-manager and find out that I didn't tell the "truth" about my employment dates, am I screwed? Is this mistake minor or can it be understood as detrimental and would question my integrity?

This is irrelevant to the topic, but if a company sends me an email stating that I have one last interview with them and says towards the end that I come prepared with my summer schedule to discuss starting dates. Could I assume that this is an offer? They also wanted me to read and fill out a lot of forms and have them completed and with me at my last interview. Sorry to ask these paranoia questions, I'm just anxious.

Thanks for reading and I'd appreciate the feedback.