I am wondering if a criminal record check is part of the VISA appliation for China. I am concerned about being denied.
You will be asked about your criminal record on the China visa application:
Section 3
3.1 If you have been refused for a Chinese visa in or out of China, please select YES. Otherwise, please select No.
3.2 If you have been refused to enter into or been deported from China, please select YES, please select No.
3.3 If you have any criminal record in any country including China, please select YES. Otherwise, please select No.

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Recent real life experience:

I checked the box saying that I have a criminal record. I also wrote a "detailed description" as requested. For the description I played down the crime and focused on my remorse for the situation and how it's been over a decade since the crime. When I say I "played down" the crime, I mean I said "I stole money from a store" instead of giving details or specifying the offense.

To get the visa I applied in person rather than by mail. The interviewer read the description in front of me and my wife, then asked her co-worker something in Chinese while looking at my paperwork, then told me to pick up my visa in a few days: as easy as that! I've already picked it up and I'm ready to go.

The law seems to always use your past against you, even if you weren't 18. A license to carry tends to check your background for felonies and domestic issues. Even so, if the background check goes through to purchase a handgun here, you will most likely be able to carry concealed.