I'm not a huge fan of battle systems or 'sims-like' family things, as far as the shop keeping track of such things.
However, that being said... c:
You are more than welcome to RP your characters as having a family. Two human characters could start a family and have children, get married, etc -- the whole gambit. Whether you decide to make those characters's children playable or not would be up to you. Just keep in mind that, ICCly, the shop's timeline would apply to children as well -- so if they have kids just starting at the beginning of the meta plot they wouldn't magically grow up to be adults overnight.
As for work, the setting generally reflects that of a typical early 1900's world with only a few major differences (gender equality being one, and more open-mindedness and forward thinking in general) but technology is what you would expect to see between 1900-1920.
As for starting a group, not sure what you mean? If you mean some weird religion, occult, or band of gathered Summoners, then yes to all of the above!
Basically, as long as what's being done sticks to the limits of the setting itself (technology wise, mostly) it should be fine. c:
Edit: Also, I highly recommend reading through the guild at this point. Most 'extra' info pertaining to the setting has been written and posted. Though I certainly welcome any and all questions that this info may not have covered!