If you have SELinux enabled you are going to get a lot of issues very quickly if you change any of the default locations or users. It seems this would be a likely cause. Use getenforce to get SELinux status to see if this is the cause.
/home/db is owned by db mongod may need to be configured to run as this user.
and/or mongod does not appear to have write permission on /home/db .
Deviating from a standard setup will expose you to many configuration items that are configured by default.