To answer your first question the law does not indicate what type of holster you need to carry in. It does not even require a holster to carry. There has been a court that has indicated, the fishorman case, that mexican carry with the hammer back could be considered as a type of carry to warrant alarm.
The second answer is if you live within a city's limits then you can apply at the local law enforcement office or the county sheriff. If you live in the county then you must apply at the county sheriff.
"(13) A person may apply for a concealed pistol license:
(a) To the municipality or to the county in which the applicant resides if the applicant resides in a municipality;
(b) To the county in which the applicant resides if the applicant resides in an unincorporated area; or
(c) Anywhere in the state if the applicant is a nonresident."