I would like to know if all the Maturity Level 2 Process Areas must be completed for a Maturity Level 2 appraisal? There are some process areas which are not applicable to our organization.
For the CMMI for Development (CMMI-DEV) there is only one Process Area (PA) that can be designated Not Applicable (N/A), SAM. Therefore, at a minimum, REQM, PP, PMC, MA, PPQA, and CM are required for a Maturity Level 2 (ML 2) appraisal. And if the organization has outsourced some work, then SAM is also applicable.
I find it hard to believe that you can state that one or more of these PAs are not applicable to your organization. Every project has requirements to manage from the janitor to the President. Everyone works on a project. You just have to define what a project is. And then you manage the project. Everyone can define specific measures that can be used to manage the project. Everyone has some sort of configuration items or documents that have to be managed. And everyone needs some sort of objective evaluation of the process and project compliance. For a small organization, you may have combined one or more of these PAs under one person. But that does not mean these PAs are not applicable.
Now if you said that you had problems with the engineering PAs (RD, TS, PI, VER, and VAL), then I would suggest that the CMMI-DEV may not be the appropriate model constellation for your use and you should look at the CMMI for Services (CMMI-SVC) or CMMI for Acquisition (CMMI-ACQ).