Is it considered impermissible (haram) for a questioner to engage in e-commerce using the resources of his father's bookstore (house, office, computer, phone, fax, car) to strike deals selling books to new customers who had not previously dealt with the original bookstore, especially after being repeatedly expelled by his father, given that he is generating additional income for the bookstore through these efforts?

Your question contains two parts: The first concerns the problems between you and your father. We advise you to be patient and seek reward from Allah, as honoring one's parents is a great obligation and disobeying them is one of the gravest prohibitions. Try to be gentle with your father in speech and dealings, and mediate through someone who can advise him to reconcile your differences.

The second matter concerns buying books from your father's library and selling them: This is permissible in itself, but using the library's tools (devices, car, shop) without your father's permission is forbidden. If your use of these tools was without permission, then your profits belong to you, but you must seek your father's forgiveness. If he does not forgive you, then you must pay rent for the use of his belongings at market price.