If you're using a Standard or Advanced license, then yes, you can easily convert a polygon into a metes and bounds description via one of two methods.
First relies on the COGO tools, specifically Traverse. In edit session, double click the polygon in question to enter vertex editing mode. Launch the Traverse tool on the COGO toolbar, then right-click in the call box and choose Load Traverse from Sketch. This will create a list of calls for the polygon which you can then save to a text file. Note that the start coordinate will be based on the polygon creation, and that it won't cover the commencement calls to that PoB.
Since you're wanting attributes on lines and points, you'll need to break the polygon down as ed mentions. You'll need two different feature classes, one for points and one for lines. Getting points from vertices and adding coordinate attributes to those points is covered at other questions, as are getting the distance/direction attributes on the lines (which also uses the COGO toolbar and is discussed at How to display survey calls using the traverse tool?).
The second method involves using Parcel Fabrics and is considerably more complicated. Basically you import that shape, but all the information you're looking for is already tracked in a parcel fabric.
As an aside, you mention this is for 'local government legal requirements'. You don't mention where you are, but in some places and circumstances, generating metes and bounds descriptions for such records can only be done by certain people (licensed surveyors) and may potentially open you up to a host of liability issues.