Grammar pattern: 在......(之)下

Hi! I have a penpal who wrote this sentence "我曾经在大家帮助下，钓了一条比较大的鱼。". I need help to translate it. I get the general meaning of it but can't figure out the details. E.g. 1) This grammar pattern 在......(之)下 is apparently used in the sentence but I don't realize the meaning of it. 2) Why 曾经 and not 已经? 3) 大家 refers to a group of peolpe, in this case my penpals relatives (if I got it right). Is it common to call the family 大家?