Is zakat obligatory on a sum of money that has been held for a year, knowing that it is awaiting use in a new project, and is it permissible to give zakat to siblings who have good salaries but perform household chores?

Zakat is obligatory upon you because its conditions have been met: reaching the nisab (threshold) and the passing of a hawl (lunar year). It is permissible to give zakat to your siblings if they are poor, and doing so entails a greater reward. However, if they are wealthy, it is not permissible to give them zakat, unless one of them is indebted, in which case it is permissible to give him from the zakat to pay off his debt.