Star San does not melt vinyl hoses or render them unsafe in any way. I use Vinyl hoses (just called my LHBS to verify the hoses I buy there) and leave them in buckets of Star San for sometimes hours at a time while brewing, as they await use. Where did you read about this? I don't know of any brewing equipment that star san can't be used for.
Off the top of my head and to your questions -
Star San will not destroy a counter top once diluted (it would evaporate long before it could cause a problem). In its concentrated form, however, yes it can leave permanent marks; always wipe off the outside of the Star San bottle (sides, bottom, etc.) before putting it down somewhere. At the very least, put it on a plate or in the sink with the water running if you can't wipe it down right away.
Rinse your hands in the sink anytime you handle the bottle/dilute it, just in case you got any concentrated star san on yourself.
I second the note about it drying out your hands. It did for me at first, too, but like Lando, my skin no longer reacts to it at all. I dilute the recommended amount on the bottle (1 oz to 5 gallons water).
Star San's active ingredient is the same acid that's in soda (phosphoric). Yeast will literally eat it. It has no flavor, and some people have racked beer on quite a bit of Star San with no adverse affects, specifically to flavor. I believe John Palmer was one of the people who did a test like this.
It does not affect head retention.
Don't fear the foam. I frequently rack beer onto tons of bubbles/foam that won't drain from a carboy (Star San tends to foam up a lot when shaken/disturbed). No issues at all. The foam helps, if anything - if would-be infection does fall into a carboy, the bubbles are enough to kill it. Don't spit in it to test or anything, but you get the idea.
You can mix up to a concentration of 1 oz to 3 gallons and still be no-rinse. Any more concentrated than that requires rinsing. But, just stick with 1 oz per 5 gallons; 1 oz to 3 gallons is overkill unless you're currently fighting a house germ that's been infecting all your batches.
Tap water (especially hard water) tends to make Star San foggy/cloudy. It doesn't last more than about a day in most ~100 or so ppm tap water. Once star san's pH goes above 3.0, it is no longer effective as a sanitizer. The cloudier the solution, the higher the pH probably is. Now, if you dilute Star San with distilled water or RO (reverse osmosis purified) water, it can last months and months if you only put pre-cleaned items into it (e.g. don't take a hydro reading, empty the thief and then drop it in the star san bucket). I buy 5 gallons of distilled water at the grocery store, keep in a 5 gallon work bucket with lid. Your Star San will last much longer this way, and it will save you money in the long run. If you steal Star San from the bucket, only put it back if you've kept the stolen portion clean.
Water first, then add the Star San, and stir in gently. It mixes readily and the less you splash it the less foam you will need to deal with. Foamy buckets can make hydrometer readings hard because the foam will block your view of the hydrometer in your thief.
Star San is not sticky.
You only need to soak for 30 seconds to sanitize (per the creator of Star San). It says a minute on the bottle because it has to by law. It's not a minute; it's 30 seconds.
Invest in a spray bottle. Fill with diluted distilled-water star san and use it to sanitize things. You can reuse it for months and months. Also, you can unscrew the top and use it to fill airlocks. Much safer than filling with water; similar to filling airlocks with vodka.
If you buy one extra 1 gallon jug of distilled water, you can eyeball a dilution of about 1/4 to 1/5 of an ounce. Mark the jug so no one drinks it and use that for small sanitizing projects like soaking airlocks and rubber bungs in a bowl.
Yes you can store Star San in other plastic containers like soda bottles, etc.
You will splash diluted Star San in your eye at some point. Don't panic. Just flush with water for a minute. I've done this to myself at least twice (I'm an idiot); I can still see fine.
Star San is only effective when wet. If you sanitize something, then let it dry, it is no longer sanitized.
Good call on the vinator. Vinator + star san + bottle tree = easy easy bottling. Drop the caps right in the vinator bowl, and pick em out as you go.
Here's an interview with the creator of Star San that you will probably find very informative. They also discuss bleach.