The options that are set regarding timesheets won’t be affected by the security mode, but of course security permissions will be different. You will need to make sure that permissions are set properly.
As long as the projects haven’t been deleted then the assignments will be there. I don’t know if or what the limit is for OData but you can assume that if the data exists that you will be able to access it through OData. The limits are much higher than Project Server’s needs.