1) You can add an object ACL for CheckIn / CheckOut for full rights. Add a check mark for CheckIn / CheckOut.
Then you can also go in and delete it here. Do not forget to restart SE after changing the permissions.
2) You can try creating a new revision in SE by logging into Teamcenter as infodba
3) I still do not really like the idea of doing a second revision for the template, usually the existing template is updated or added new (in the new Item) - so usually I do for NX. With SE, I did not work, maybe there you can do revisions for template.