Your referring to the '*' change decorations familiar from SVN and CVS plugins? If so, and if you're new to Git, keep in mind that there are two change states in Git, staged and unstaged. EGit uses different decorations for the two states. Files with staged changes get a '*'. Files with only unstaged changes get a '>'. If a file has both staged and unstaged changes, it gets both decorations.
Do you see the branch-name+status decoration at project roots? If you don't see those, that probably means you didn't do the import correctly and the projects are not being managed by EGit at all. But in that case none of the EGit operations would be available.
re: plugin conflicts, I have workspaces that use both EGit and Subclipse and I haven't run into any issues. Can't say for sure about Subversive - I never liked it and never used it for very long -- but I haven't heard of any problems like this.
I don't see any decorations at all, including branch-name+status at the project root. However I'm sure my folder is being managed by EGit because 1) I used it to create the repository, and 2) it is performing the add/commit/push commands correctly.
When you say EGit is performing operations like add, commit, etc, what view are you in? Specifically are you in a code-editing view when you run these, or are you doing these things from the the "Git Repositories" view? You can do the latter without ever importing at all. So if you import in the wrong way you can get yourself in a state in which the editing windows are not managed by EGit, but EGit operations can still be performed via "Git Repositories".