Am I eligible to work in Beijing, China?

I hope this one can be answered, as I am getting a bit worried. Long story short is this: since Dec. Protected content , I have been employed full-time at my dad & grandfather's company. I was basically an office assistant - doing researching, writing and editing reports, etc. I didn't graduate from college until August Protected content , meaning I was working fulltime both before and after graduation. When I traveled abroad since Sept. Protected content months in Cambodia and 1.9 months in China), I was doing this work, still full time, online; was a way of still being employed while I was overseas.

Now a Chinese company wants to hire me. (doing basically the same thing). Will this type of work I did before - including fulltime online work - hinder me from being approved for the Foreign Expert Certificate, or will I still have a good chance? I am just worried that because I worked for a family-owned business and pretty much 2 years of online work while I was abroad.

I must also mention too that before that, I worked for a few years part-time doing customer service then full-time as an Assistant Manager at a retail store (still while in college).

Also, I have heard from several sources - including the company that wants to hire me - that a State-wide Criminal Record Check (done by my state's law enforcement agency, not the FBI) will suffice for the Criminal Record check. Is this true?

Any feedback would be helpful. Thanks.