1. The first point I am unsure about is how people are drawn to them in the first place. Is is a sort of calling, or is it more of a choice or aspiration?
In San Francisco in the 1980's, Third Order Seculars were called SFOs (not related to the airport.) One summer I went to the city fair and came upon a booth manned by SFOs. They were helping city authorities find housing for the homeless. They invited me to join them but I hesitated. Later, I visited St. Boniface Church, a downtown church staffed by the Order of Friars Minor (OFM). I saw a statue of St. Francis there and prayed, "If you want me to join your Third Order, you'd have to give me a clearer sign. Not long after that, I met a nice man who was an SFO. I married him and he took me home to his house near St. Anthony's Church, also staffed by OFMs. We were both active in the parish and all our friends were SFOs. What could be a clearer sign?
2. From my understanding, there are regular and secular members of a Third Order.
You are quite right. Third Order Regulars are religious, meaning they have a Rule to live in community. Third Order Seculars are mostly lay people with a few Diocesan priests in our ranks. The late Pope Paul VI was an SFO, so was St. John Vianney. The Franciscan Third Order Secular was the original Order that St. Francis founded, before the men started living in community to form the First Order (OFM, OFM Cap, OFM Conv). There are many historical figures among the Seculars, some were even royalty: St. Louis IX King of France, St. Elizabeth Queen of Hungary, St. Thomas More, Christopher Columbus, Franz Liszt, Michaelangelo, among others.
I don't know much about Third Order Regulars, but many of them have formed into numerous other branches of the Franciscan family. Out here, for example, there's the OSF (An Order of non-habit-wearing Sisters who live in apartment houses, who are into social justice, saving the rainforest, anti-gun lobby, pro-labor unions, women's ordination, and liberation theology in Latin America. They work in chanceries, parish offices, and church charities and dedicated to inflicting pains in conservatives' and traditionalists' behinds.
A long time ago, the OSFs, too, wore habits. St. John Neumann, the first Bishop of Philadelphia, founded an Order of teaching Sisters of St. Francis in his diocese. The new U.S. Saint, St. Marianne Cope, was a Third Order Regular who worked with St. Father Damien tending to lepers in Molokai. I think the difference between a TOR nun and a Poor Clare nun is that the TOR is active while the Poor Clare is contemplative. Also Poor Clares are Second Order and live in monasteries (like Mother Angelica and her Sisters.)
3. If they do live the same, why would someone be a regular member of a Third Order rather than taking the half-step more?
I don't think TORs consider OFMs a "half-step more." I think it's a difference in charism. TORs are an active branch. OFM Caps (like Padre Pio, Father Solano) are contemplative and they live in monasteries. OFM Conv (like St. Maximilian Kolbe) are more like missionaries. OFMs (neither Caps nor Convs) are a combination contemplative/active branch.
4. It is obvious that not all Third Orders could have a presence in every corner of the Earth. Does any Order that has a convent and/or monastery in an area have the potential for members of a Third Order, or is there separate/additional administration required that may not be present?
Yes, that's how it usually goes. Third Order Secular Franciscan fraternities are usually attached to a community of the First, Second, or Third Order Regular because their Spiritual Assistants must come from those communities. Third Order seculars also have nation-wide and international organizations with officers, etc., and they hold congresses and print newsletters and network among themselves. No one knows exactly how many Franciscan Third Order Seculars in the world.
5. I was wondering what kinds of activities/practices members here were involved in.
After Vatican II, Pope Paul VI rewrote the Rule of the Secular Franciscan Order and just like the changes brought about by Vatican II (I didn't say "Spirit of Vatican II," did I?), there were many interpretations on how best to put it into practice. All agreed that the #1 duty of members is to attend a monthly meeting where they pray the Liturgy of the Hours (usually Sunday vespers) in community. World-wide leaders also agreed forming four working commissions, just to add to the fun, travels, and parties: Family, Work, Environment, and Peace & Justice commissions.
The best places are for those in NGOs who sit at United Nations conferences, etc., presumably lending their expertise on these pressing social issues. But our St. Anthony Fraternity was small, so all work was done in small scale: Serving at the soup kitchen, tending the friary's flower garden, setting up toilet facilities for illegal migrant laborers, marching in anti-war or anti-nuclear demonstrations, marching in the West Coast Walk for Life. There's also a committee in charge of formation (teaching basic catechism to candates. I was in that committee, so I didn't have to work in the social justice commissions.
Five years ago, my husband and I moved northeast of SF to an area where there are more Dominican houses than Franciscans, therefore all our friends here are Third Order of the Preachers (I think that's what they're called - TOP). My husband was very sick and later died. The closest SFO fraternity to me is in Napa Valley, but since I don't drive, I couldn't attend the monthly meetings. So now all the connection I have with SFO is my Liturgy of the Hours.
Pax et bonum,