Yes—parts like this are commonly removed with a two-pin tool, such as a lens spanner, caliper-style tool, or even fine point tweezers if they fit securely. The main caution is that the piece can mar or deform easily, so use a properly fitting tool and only light force. A friction method with rubber can sometimes help start it turning. Be careful: thread direction may vary by camera model, so don’t force it if it doesn’t move easily. Also confirm the bottom plate isn’t actually being retained by something else, such as the battery cover.

For the mirror lock-up issue, adding oil is generally not recommended. On older film cameras, sticking is more often caused by dried grease and dirt rather than lack of lubrication. Cleaning the affected linkage carefully with a small amount of lighter fluid or electronics cleaner on cotton swabs is the safer advice given, while avoiding excess fluid that could migrate onto the shutter.