Thanks so much for posting this info! Super duper helpful! How long did you cycle your tank for? I started a 5 gallon pico and did dry rock and arag alive sand. I want to start putting corals but have heard of people running a cycle for 6 months. What did you dose to get your beneficials colony?
You aren't understanding the term "cycle". We are referring to the nitrogen cycle. When you "cycle" a new tank, you are allowing an adequate amount of nitrifying bacteria to colonize the biomedia so that any fish waste, extra food, etc does not harm the tank inhabitants -- food and waste breaks down to (among other things) ammonia, which can be toxic to fish and some inverts. Nitrifying bacteria converts ammonia into nitrite and nitrite into nitrate. Nitrite and nitrate are essentially harmless to saltwater fish, although there are good reasons to control their level to some extent. You want to add fish in a manner that allows the bacterial population to keep up with the increased bioload.
Coral, on the other hand, uses forms of nitrogen (ammo, nitrite, nitrate) as food. While too high a level
can be harmful to coral, coral itself does not significantly add to the tank's bioload and adding coral will not increase the ammonia level... again, getting rid of the ammonia is the reason we need the tank "cycled" before adding organisms that can be harmed by it.
Several factors affect how successful a person may be with coral. Tank size can be important to take into account as the smaller the tank, the more intensely any changes in water chemistry will affect it. Larger water volumes are more forgiving since anything added to the system will be more diluted.
Tank age is also a factor, and this may be what you are thinking of re: waiting 6 months. A new tank, especially one started with little biodiversity (e.g. dry rock, etc) can take longer to mature to a point that the water chemistry is stable enough to allow corals to do well.
As you can see, a small tank that's new will generally be more unstable than one that's older and/or larger (larger tanks still need time to stabilize though).
Regarding your last question, in a 5 gallons tank, water changes will be simple and regular water changes will likely be sufficient to replenish things like calcium and magnesium that corals use. If you end up progressing to keeping high need SPS, you might need to supplement some, but starting out, there's no need.
(A word of advise about dosing -never dose anything you're not testing for.)
Hope this helps!