Is delaying the transfer of money to an Islamic bank and calculating zakat considered a sin, and do I owe zakat for the years from age 17 to 21 if my mother did not pay it?

You must withdraw the money immediately from usurious institutions and quickly close the interest-bearing account to get rid of it and pay the obligatory Zakat (definition) immediately. If the delay is due to an excuse, there is no sin; otherwise, there is. Zakat is obligatory on your share of your father's money once it reaches the nisab (definition), starting from the date of his death. Your mother's payment of it without your authorization does not waive it, and you must pay Zakat for the past period. The law not allowing you to dispose of the amount does not waive it. The age of legal puberty is not 21 years.