Ticks is done in source side, also think of ticks for the count min and count max of RealOTS, and cycles as the amount of cycles left for the condition to end.
Right. Count goes down each second until 0, after which cycle is decreased by 1 and count set again to count max. And so on till no more cycles left.
For example, utani hur sets cycle = 6 and count = 10, which results in (10 + 1) * 6 = 66 seconds of total duration. Utani gran hur has 4 cycles, so 44 seconds (speaking of 7.4, since 7.6 it was shorter by half because of mana system update).
Some conditions are also made that the effect is weaker the less cycles left, e.g. light or drunk.
Light spells have cycle = radius and count = duration/radius; for utevo lux radius is 6 and duration 500. This results in 6 cycles of 84 seconds each (500/6 + 1), where after each cycle radius is decreased by 1 (so the light gets smaller). So, in total it lasts for 504 seconds, though you don't really see the last 84 seconds with radius = 1, because of the small light built in the client (others can still see it around your char though).
Ok. Not sure what most of those mean, but noteworthy for sure.
SkNr is skill number, Act is the actual value, Max and Min are exactly what they say, DAct and MDAct are modifiers for Act (items, spells), Cycle and Count as explained above, AddLevel says by what value the skill (Act) is increased upon advancement, Exp stands for the current experience points, FactorPercent is a multiplier to calculate exp needed for the next advance, NextLevel is the experience needed for the next advance, and Delta is also used to calculate the exp needed (it's a starting point in general, e.g. for melee fighting it's 50, for distance 30, shielding 100 etc.).
About those modifiers, the funny thing is that cip probably forgot to take them into account in SkillProbe function (based on skill). It's not a major bug (if it's even a bug), but it means that when you have an item that increases your skill, it will not have any effect in that function. E.g. if you'd have an armor that increases distance fighting - it would increase your damage, but NOT the hit chance. Or if you'd have an item that increases fishing skill, it wouldn't do anything at all, though you'd have a higher skill in your skills window.
Of coruse that was in 7.7, they could have fixed it already. In that version such armors didn't exist, and the only scenario that I can think of is destroying those stones with a pick - the chance is based on axe fighting and axe ring wouldn't increase it.