League-of-legends – What are Katarina’s abilities’ damage type

Runes, as well as items like Sorcerer's Shoes and Haunting Guise offer FLAT penetration (i.e., you ignore up to X) of your opponent's MR.

The "average" champion has a base MR of 30, that doesn't increase with levels. With ~9 MR penetration from runes, sorcerer's shoes are enough to bring that down to basically zero.

The other options are reduction (triggered by champion abilities like Amumu, Ryze, or Fiddlesticks, or the Abyssal Scepter) which actually decrease your opponent's MR (and so stacks with penetration) and % based (the talent and the void staff). Of these, Reduction is the only way one can bring your target's MR below zero.

When a single character benefits from one or more of these, they are applied in this order:

1. Flat Armor/MR Reduction
2. % Based Armor/MR Reduction
3. % Based Armor/MR Penetration
4. Flat Armor/MR Penetration

Some of the above information can also be found in the game mechanics thread on the official LoL forums, here: http://www.leagueoflegends.com/board/showthread.php?t=3287

The answer to your question would then become:

54.36 MR * .85 = 46.206 MR - 8.55 = 37.656 effective MR. (I don't know the formula off hand to convert that to % damage reduced)

LoL has some inconsistent wordings, I'll agree.

Bonus health means health gained from items / runes / masteries.

At level 18, Shen naturally has 1958 health*, so Ki strike bonus damage is equal to (Total Health - 1958)*.08.

*Shen suffers from a reduction in health due to the Inverse Ninja Law when Akali, Kennen, or both are on his team. This will reduce the base health of all involved by 1 or 2, giving Shen a range of base health from 1956-1958.