Grammar pattern: 在......(之)下
zhenlijiangJune 11, 2010, 11:21 AM
1) You can think of it as the prepositional phrase "with ~", in this case "with everyone's help". 在～下 is the conditions if you will, under which what you're describing is happening/has happened.
2) 已经 would be already. 曾经 is once, one time.
3) I would think you could certainly call the family 大家, but hope you hear from people who can tell you how common it is.