Why are these ranked #1 in the category "Fishing" ?

When a company puts a product in some obscure category, they can get the "best seller" icon when they inevitably get more sales than the other products in that category. That's how you end up searching for something like "guitar strings", and multiple products show up as the #1 seller. Why Amazon still allows this after all these years, I will never know.

Do all 6 strings come in the "1 pack"?

If you note on the front of the package, it has a list of numbers (10, 13, 17, 26, 36, 46 on the "Regular Slinky" set, and similar on others). These are the string gauges included in the pack. If there were only one string in the pack, it would list a single number, because you'd have to know which string it was.

what is the difference between slinky and non slinky?

Slinky is just a line of strings from Ernie Ball, the "Slinkier" they are the thinner they are, regular Slinky are 10 gauge strings, super slinky are 9s, and "Not Even Slinky" strings are 12s (the number represents the gauge of the lightest string in the set).

I'm looking for extra strings for my new Les Paul Special II. I'm buing guitar from amazon, it costs $149. Are this strings compatible?

Short answer, yes they should be fine. Long answer, the comparability between strings and guitars doesnt matter, its the string slots that in the nut that matter. The les Paul's usually use bigger strings anyway.