модний = fashionable, стильний = stylish
Unfashionable clothes can still be stylish.
Yes - i think both "in style" or "stylish" would be am acceptable translation.
Perhaps a native speaker could confirm (for example, that there is not a different word for 'stylish'?).
There's стильний, but it doesn't really mean "fashionable", it's rather "elegant"; decorated, dressed, made in a particular style