Are we entitled to claim compensation for the losses caused by our brother in managing our deceased father's properties, or should we be content with dividing what remains according to Sharia?

As long as your father's registration of properties to your brother was not a real sale, but rather for the purpose of managing them due to the father's health incapacity, then your brother is acting as an agent for his father. His hand is a hand of trust (amanah), and he is only liable for transgression (ta'addi) or negligence (tafrit). Experts should be consulted to assess whether transgression or negligence occurred, and to estimate the resulting damage.