After importing a content type from Features, What's the correct way to manage it?
Once the content type is created, is it part of the db as if I had created it normally through the UI?
Yes
Can I safely delete the Feature generated content type code?
No- See this Q/A for a more complete answer.
Can I manage fields through the UI...
Yes - once you have the content type set the way you want it, you should regenerate the feature module so that you have an up-to-date representation of your content type in code.
...or would I have to fiddle with the Feature generated code?
Definitely no


What's the correct workflow to work with the content type from that point?

First, make sure you have a clean starting point by ensuring that all of your features in all of your environments have the "Default" status (this just means that the loaded database configuration of the Feature matches the configuration defined in code in the Features module).


Make changes to the content type through the UI on dev as you normally would.
Once the content type has been modified to your liking, Recreate the Feature by clicking on the "Recreate button". That will generate a tar file. Extract that file in the same directory as the existing Feature module - overwriting the previous version.
Revisit the Features page on dev. The feature that was previously overridden should now be "default".
Assuming you are using git or subversion or similar, commit the changes to the Feature module and pull them to staging. (If you're not using source control, just FTP the changes to the Staging server).
Visit the Features page on staging. The Feature in question should now have a status of overridden. Click on the "Overridden" link, tick the checkboxes on the resulting page and click "Revert". This will update the database settings to match what is defined in the new Features module. The status of the Feature should now be "Default". (Note: sometimes the Features module automatically pulls in the new settings when you visit the Features page, but honestly, I'm not sure what triggers that or when - perhaps someone can add to that).
If all goes well on staging, repeat the same steps on prod.