They are very similar. The only difference is that «ш» is always hard while «щ» is always soft. To master «ш», form a cup with your tongue: let the middle of your tongue relax and lie down, and place (but don't press) the tip of your tongue against the back of the alveolar ridge (post-alveolar). Pronouncing «щ» is pretty much the same as the sh in she, but you should raise the middle of your tongue slightly higher to the roof of your mouth.
Because кошки is plural ("cats," not "cat"). "Here is a cat" would be вот кот or вот кошка.
Wouldn't "the cats are here" be "кошки здесь", while "here are the cats" is "вот кошки"?
"Look, cats!" - that was my answer. I think it should be accepted or I might be wrong? :-) Like we're passing by in car and saw bunch of cats, can you say "Вот, кошки" ?