No worries at the questions! I love answering them! It's why we have forums like this ^^
I wouldn't use salt in the big tank because, yes the other fish would be effected. Also it's cheaper when you use a small container, if you think about it you'd be using 1 teaspoon or less in a small container whereas in the 10 gallon it would be 10 teaspoons. Also daily water changes would be such a pain in the behind on that rather than a small volume of water.
He'll be fine in the small container, if it even is fin rot.
the LFS might know his age or tell you when they got him in. To me though he looks like he's about 3.5 months old, maybe 4 months. So in that case his tail is still growing out, that's why it looks small to me. So as he get's older his tail is going to grow out as well as his other fins.