Need Help Understanding 2016 Mastery Changes

Hello LoL community! I've played this game since beta but have been without a computer for around a year. I bought a laptop and have played for a few weeks now but am having a little trouble adjusting to all of the changes. I am hoping that my fellow players can help me understand some of the specifics of the new masteries. All right, background info over; lets dig in!

Many of the new masteries are pretty self explanatory: the Sorcery mastery gives, "+2.0% increased Ability Power". Others don't really provide enough information. Even the Sorcery mastery doesn't explain if it's 2% of your base AP (I assume so) or bonus AP or even Total AP.

The Merciless mastery lets you "Deal 5% increased damage to champions below 40% Health". If Karthus activates his ult when Soraka is at 30% health and she heals to 50% health before the damage is taken, does it still do extra damage? I would think not, but I'm not 100% certain either.

The Assassin mastery provides a 2% increase in damage dealt to champions when no allies are 'nearby'. Checking the LoL wiki reveals that 'nearby' translates to a range of 800. Can I assume that the information on the LoL wiki is accurate and current? And what counts as 'damage'? All sources of damage, including AD, and AP? Is it only direct effects like a skill shot or do Yoricks Ghouls also have increased damage as one of his abilities? When Karthus ults does his ult deal increased damage to the lone champion at mid with him and normal damage to champions elsewhere in the map and outside the 800 range?

For most of the masteries I'm assuming that the numbers refer to an increase in the champions base numeric values, before any other modifiers are applied. But that still leaves me with a lot of questions and an incomplete understanding of just how all of these masteries work. If there's a database or in-depth forum post with Riot-verified information on this I'd appreciate a link to it.

Thanks for your time.