Dumb question..?

i found a lot of plastic parts that i thought were unnecessary or at least compared to other cars i've seen. 
 

The battery goes through many hot and cold cycles in its life...and with heat being the biggest killer of electrical components, thats why its best to keep it cool.  The battery can get rather hot when it is being charged along with underhood temps from the exhaust manifold and a hot radiator.  Basically, heat = resistance and resistance = shorter life of electrical components.

I kinda liked the CAI on the Battery

I was gonna say was bkey71 has already.
In short, if there is no good reason to remove it, leave it on there.
I have actually removed the triangular side mount (w/the Fisher-Price style hardware) and smoothed out the side of the snorkle.  I have no problems w/noise or rattling and it makes it so much easier to remove when needed.
 
 

wow i never knew that...well that means that is staying on. I took that fisher price piece off the same day i baught the car I looked under the hood and said wtf and there is a door on that piece that i still havn't figured out what its for but who cares it made it easy for me to change the side signal bulbs. 

i took mine off months ago, but only cuz im too lazy to put it back on lol, plus i have some extra wires in there, so i have to notch the cover to get it to fit again.

Yeah, what is that little door on there for?  Those plastic screws are a pain in the ass....I took them out today to remove that cover (trying to get to the air box) and those things are ridiculous.  Does that cover protect anything?  I put it back on to be safe until I know the car better.

 
Nada!!  Read my post above. ^ ^ ^ 
I removed the damned thing over 2 years ago now.  It does nothing but get in the damned way.
For a cleaner look, take the snorkel off and cut/grind/sand the tabs off too.  Oh, and btw, the snorkel comes apart for easy modding.
 
 

bkey71 is correct about the battery air intake.  In addition, the cover apparatus helps keep the battery very clean, which helps avoid dust accumulation - dust is bad because it can significantly reduce the cranking power of the battery.  It also helps ensure the battery and connections stay dry, reasons why this is good should be obvious.

BTW, some people remove the engine top cover, which can be a bad thing to do.  It will extend the time your engine takes to reach the optimum operating temperature range, especially during the winter ... while the engine is warming up, it is much less fuel efficient.  And, that plastic cover can protect your hood from getting repeatedly heated to a high temp, which can help protect your paint.

Triangle side mount? Snorkel?  You lost me with the slang.  What are you fellas talking about?

I've heard the battery intake called a snorkel before (Mz3forums,) and it seemed to fit, so I use it.
The triangle-side mount is that useless POS that is supposed to hold the snorkel in place.  But as I found out is not really necessary as the batt box and rad support do that just fine w/o it, and only makes accessing the battery/air filter box/lights and ??? that much harder.  Plus as 2.0(?) mentions, those plastic screws/clips are not only a PITA, but stupid. 
 

Thanks V.  Makes sense.  Though I have experience with fixing and replacing this and that on many cars over the years, I have not touched much of anything in my M3 engine compartment.  I have accessed the battery a couple of times to reset the CEL light, and therefore I know what you mean by snorkel.   I have not removed anything from my engine compartment.  To be honest, modern cars are so electronic (versus being very mechanical in the late 1970s and earlier ... I in my past owned some POS 1979 and older vehicles ...), I'm almost scared to touch anything in the engine area, other than to check fluids, for fear of Fing something up.

Believe me, I know what you mean. 
I have been trying to update my info and learn some new tricks on these forums for a few years now... trying to get a feel for what can and cannot be done from the young techno-geeks w/these modern computer controlled cars.
It used to seem hard to come up with new and wonderful ways of improving power and mileage, but that was nothing compared to todays cars.