Great question, thanks!! When I say I don't write in the name of the Church I am being pretty literal. The Church did not consecrate me as a writer, nor did (she) commission me specifically to write. She consecrated me as a hermit and commissioned me to live a life of prayer and penance in the silence of solitude. Writing is one of the ways this life spills over into ministry, yes. Because writing is a really important part of my life and because I tend to write these days mainly about my exploration of c 603 and eremitical life, I can see where I might slide into thinking of my writing as part of my consecration and commissioning. It's a fine line, though, especially since my Director encourages at least some of my writing. Perhaps if my Bishop were to say I needed to write more, or in some way directly encouraged me to write, my position on this might change, but for now, what this all means for me is that I don't say I write in the name of the Church; instead, I live eremitical life in the name of the Church and writing is a part of that. Think of it this way, recreation and sleeping are also important parts of a healthy eremitical life, but strictly speaking, I don't say I recreate or sleep in the name of the Church!
Yes, you have standing in law as a lay person (or a person in the lay state)! If you married in the Church you also have standing in law as a married person. The Church gives certificates for the various stages or ecclesially significant moments regarding these things. You might not know this but your Church of Baptism keeps track of the various sacraments you have received and other ecclesial events in their own records. If you entered religious life and made vows, a record of that also goes to your Church of Baptism or home parish. If you (just for example) were divorced and received a decree of nullity, that too is kept not only in the chancery where it was given but also sent to your home parish and added to your baptismal record. If you are ordained a deacon or priest, the same thing happens. Thus, when someone writes for your baptismal certificate, they will receive notice of all the Sacraments you have received and any other events (e.g., ordinations, professions, and consecrations) that impact and may modify your standing in law.
And yes! so long as you have not been ordained, the Church has commissioned you to live lay life in her name. That is why you are called and able to call yourself a Catholic!! You live your entire life as part of the People of God (laos Theou) in the name of the Church. Whatever you do as a layperson redounds to the honor or dishonor of the faith and the Church. Simply being a Catholic layperson is indeed an awesome calling. Consider all of the ways lay persons bring the sensibilities, ethics, and Gospel of the Church to the world!! Their lives are far more varied than the lives of priests and religious and they truly are commissioned to be the Church for others in every walk of life. The depth and import of this vocation have been diminished today. Vatican II wrote significantly of the universal call to holiness to urge us to appropriately honor the call to be laity. Some of the Church's earliest stories help in this.