Lisa is correct on the corys (and the other stuff too, for that matter
). There is a difference between "cycled" and "established" that I'll try to briefly explain.
Cycled is pretty obvious, it means the nitrification cycle has become settled so the tank is biologically stable. Ammonia produced by fish and bacteria is used by nitrosomonas bacteria that create nitrite, and nitrospira bacteria use the nitrite and nitrate results. The nitrate we remove via weekly partial water changes. Adding live plants improves this, in that the plants grab most of the ammonia ahead of bacteria--which is why new tanks with lots of plants can have fish immediately with no noticeable "cycle"--and because the bacteria will be out-competed by the plants for the ammonia/ammonium, nitrite is minimal as is nitrate. Only if there is a major biological issue will nitrates rise above 20ppm and usually in planted tanks will be much less than this.
"Established" should occur sometime after the above cycling (in the absence of plants, otherwise there is no cycle). It varies depending upon the aquarium--volume, type and number of fish, live plants, wood, and water parameters all influence this. Usually within 2-3 months if no major tampering is done and the tank is allowed to settle naturally.
Corys are often quite sensitive to new tanks, and Corydoras panda especially so in my experience. This is rather interesting, considering this is one of the species that is today commercially raised, and most would expect tank-raised fish to be a bit more "hardy," but not with these. I myself have lost several adding them to fairly new (within a month) tanks, but in tanks older than say 6 weeks, no issue.
A comment on another point you made, that this tank will only house the Ram and corys. I would suggest some "dither" fish for the upper level. All SA cichlids can be somewhat shy on their own, especially as you will only have one [and I agree with 1077 and Lisa that two (unless a compatible pair) would be ill advised for a 20g]. And Bolivians spend all of their time in the lower third of the water column; mine never surface even to feed, only eating from sinking foods (along with the corys). A group of smallish characins would be nice, 6-7 as they are shoaling fish; neon tetra or cardinal tetra [which depends upon water parameters] or one of the Hemigrammus clade [Hemigrammus or Hyphessobrycon species]. Many of these are in our fish profiles [second tab from the left in the blue bar above, or click on shaded names in posts]. Avoid active species that need more swimming room.