Yes they can share info but they're very good at finding things out without the help. I'd suggest answering every question asked honestly and don't worry about it. The BI has the ability to factor in any new changes that would influence their decision. What's done is done. I will say this. Get caught not providing info and you'll never be hired by anyone.
BTW, one thread for all this is more than enough.;)
"...Our natural, inalienable rights are now considered to be a dispensation of government, and freedom has never been so fragile, so close to slipping from our grasp as it is at this moment.” Ronald Reagan
"Those who beat their weapons into plows will be plowing for those who don't."