With all due respect, perhaps you should sell your gun and take up golf.
Firearms use a propellant to send a projectile down a barrel and exit into the ambient atmosphere, on its way to some target select by the shooter. The "fire" you are seeing from time to time is simply the burning of that propellant as the projectile leaves the barrel. Slower burning propellants = more "fire".
As for smoke, it had better not be black otherwise there could be other factors at work. Unless you are shooting a black powder firearm, the color should be bluish/grayish and not too much of it (depends upon the type and quality of the propellant used in the ammunition).
What is it called. Does it go by different names. Does each gun have a metric describing the smoke and fire content.
I hardly know how to answer this question.
It must stay in the air for awhile around me. Is it harmful to my eyes, lungs, or skin, and what should I do about it.
It can linger a bit depending upon the range and other factors (if indoor, ventilation... if outdoor, wind speed).
Do gun ranges do something about it to keep the air circulating etc. Do the gun ranges themselves have a rating.
See above for the first question here. I have never seen nor heard of a range rating system.
Do I have to worry about taking a shower and washing my cloths after shooting. What detergent should I use.
Tell me you're kidding with this one.
On my end, I do know that I can better fire after exhaling a breath.
You should not hold your breath when shooting unless you are going for serious precision and then you only hold your breath just before pulling the trigger (you let it out then hold for that final second).
My friend, you need to spend some time on several different ranges as an observer to see what other folks do. Try to glean some experience and answers to your questions be watching people who appear to really know what they're doing. The shooting sports have been around a long time and I would imagine most people steeped in the gun culture (I am one) have fired many tens of thousands of rounds of ammunition in a variety of calibers and designs and are none the worse in wear for it. Quite the contrary, it has enriched our lives, given us enjoyment and fun, and offers the side benefit of making us better at something that can be quite an exact discipline. I've been at this for 45 years and the God willing, will be at it until He takes me to my final reward.
So to reiterate, visit some shooting ranges, do some reading and other research, and take a quality course of safety and the use of firearms for you own sanity and satisfaction.