Is it permissible for me, as a born Muslim, to independently delve into profound research on Islam and explore Christianity, including purchasing and reading the Bible, with the intention of understanding our differences?
You need first to understand your own religion and study its principles and foundations before delving in other religions. You must study properly under an able scholar and be sure and firm about your faith, then delve in other religions. This is to protect you from misleading propaganda of others.
Wassalam.