Is it permissible to deal with the American bank "University Islamic Financial" (UIF), which is endorsed by several imams and Islamic organizations, to ensure its transactions are free from usury, given that details of its transactions are available on its official website?

We cannot judge the aforementioned bank negatively or positively merely by looking at its website, but the fundamental principle is that Islamic banks operate according to Sharia (definition). As long as the bank has been endorsed by Islamic organizations and imams, there is no harm in dealing with it; it is preferable to usurious banks. There is no excuse for dealing with usurious banks when an Islamic bank exists. If any Sharia-forbidden aspect is found in its transactions, it should be pointed out for rectification.