I'm not going to try to recreate my myth-by-myth comments (don't worry - technically they're all properly described) but I'll offer this comment:
There are aren't 12, or 10 or 5 myths about equalization. There's only one myth:
"There are no 'myths' about equalization, only collections of common practices that can be misapplied in a given situation if you don't understand what you're trying to fix or improve."
To this end, I offer up a article I wrote a couple of years ago about Filters and Equalizers
that will help you to understand what several types of filters (the technology) and equalizers (the products) do and how their controls affect the signal that passes through them, in both good and bad ways, and things that are traded off.
Room acoustics, and attempting to fix them with equalization, is a different problem that has mostly wrong mythological solutions. You can't effectively fix reflections and the peaks and nulls that they create with an equalizer. However, you can use equalization to correct for the low frequency buildup when a speaker is too close to a wall or corner. That's why so many powered speakers have a low frequency EQ switch or control. The reason why there's a corresponding high frequency switch or control is because users who don't understand the reason why a low frequency rolloff can alleviate a problem expect there to be one. And also, because some may find the tweeters to be harsh and can work more comfortably without those annoying high frequencies. The sometimes-offered explanation for high frequency speaker equalization that it compensates for overly reflective walls - too many high frequency reflections - or overly absorbent materials - too much high frequency absorption - is about as close to an EQ myth as you'll find. Use it with care.
And unless you're mastering or cutting lacquer, don't worry about linear phase or FIR equalizers, just use what sounds best if you have a choice, but remember to listen for unwanted frequency response irregularities due to latency and its potential for comb filtering when your recording has more than one source (leakage) for the sound you're EQ-ing.