On the Geodatabase side of things, have you granted the ArcGIS Server Account read/write access to the FeatureDataset or FeatureClass?
In Catalog, under database servers, under your geodatabase, right click the feature class point to Manage and click Privilages.
Have you registered the database with the ArcGIS Server data store?
In Catalog, under GIS Servers, right click on your server and click Server Properties. CLick the + to register your database there.
Have you created a feature template in ArcMap before publishing?
As you share, does Analyze show any warnings?