For CCDW, you would do best to peruse the Kentucky State Police's website, as they are responsible for administering the licenses.
In regards to the question of time frame, to be eligible to apply for a CCDW, one of the requirements is to be a Kentucky resident for at least 6 months. Obviously there are other requirements as well.
(from the page linked above)Be a resident of Kentucky for at least six months prior to filing the application or a member of the Armed Forces of the United States who is on active duty, who is at the time of application assigned to a military posting in Kentucky, and who has been assigned to a posting in Kentucky for six months or longer immediately preceding the filing of the application; and
Everything else you'll need to know about legal CC in KY is on that page.
As regards to your OC question, there is no time frame. Any person who is not otherwise barred from possessing a firearm can open carry at any time. This includes visitors to KY, new residents, and old residents alike.
Obviously there are KRS (Kentucky Revised Statutes, state laws) that further clarify where you are able to take a firearm and the options available to private business and property owners to prevent it if they so desire.
I believe there are some informative posts "stickied" to the top of the KY board. They have a lot of good information in them.