Orchid's soul burn ability deals magical damage, so yeah, magic resistance affects its damage.
I didnt get your second question though. Are you asking when an attack missed, can cleave miss? Then yes, if an attack misses, it does not cleave (note, dragon knight's ultimate deals splash damage, like ranged cleave, if dk's attack misses, the splash doesnt miss, but 50% reduced)
But if you are asking can an attack's cleave miss when the attack doesn't miss, then again no, cleave doesn't miss
Orchid amplify all incoming damage but a glimmer cape for example can only reduce the magic damage taken.
Storm still will do a lot of damage with Orchid even if you reduce his overload damage
You don't know how Orchid works. It's not like Soul Catcher. What it does is, it calculates all the damage you did and then deals %20 of it as magic damage after the duration ends. So it is reduced by Glimmer Cape too.
If you Orchid someone, and only right click him for the duration, he'll receive a percentage of that damage after the duration, as MAGIC damage, which means you have 25% innate resistance to it (well, most of the time at least). It is like Blademail - whether the damage you're attacking your opponent is pure, magical or physical, all damage that's returned to you is going to be pure, which ensures you receive exactly as much as you deal, unless you're bloodseeker and you raged yourself.
Mechanisms that calculate damage taken often switch the type of damage when they need to do something with it, like reapplying or returning it. Rearm, Maledict, Dispersion, Return, MoM, Blademail and many other items and spells convert damage type to what they need to be functional the way it's intended.
Still, for most of those mechanics, you have to thank Blizzard for hard coding certain things in the wc3 engine, likewise, the only reason cleave actually can't miss and ignores armor while at the same time being physical damage (buffs that block physical damage always work against it, hence why ghost scepter does) is that it's the exact way Blizzard had it hard coded into the engine. If it were otherwise, so it would be in DotA today, as legacy lives on, and back in wc3 days the only way to go around things that are hard coded was to actually code your whole subsystem in JASS, the scripting language used in wc3, which often meant you'd stumble onto OTHER hard coded things and try to deal with them instead.
orchid does magical dmg reduced by glimmer/pipe etc.
cleave dmg cant be missed unless you are the original target.
lustmolch, that's completely wrong - ghost scepter and decrepify makes it so you are not hit by cleave, and damage is truly physical. When omniknight's ult is up you cannot cleave anybody because damage is NOT pure, it is PHYSICAL in type, just ignores armor when it comes to calculations. Whenever you cannot be hit by physical damage, you cannot be hit by cleave, it's that simple, it's simply physical.
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^topic