You say "...staying under the shadow of Hinduism" means that you accept the Vedas as the revealed word of God. If you do not accept the Vedas as such, you are not under the shadow of Hinduism.
There is no harm in reading other religious texts or other religions. Krishna says in the Gita (VII. 7.) "...All is strung on Me as a row of gems on a thread." There is only one Religion - God. What you call religions are just sects of the one Religion. All religions belong to God; God does not belong to one religion. Swami Vivekananda said that as a result of understanding Advaita, he understood other religions better.
Again Krishna says in the Gita (VII. 21.) "Whatever may be the form a devotee seeks to worship with faith--in that form alone I make his faith unwavering." Swami Vivekananda said that every man is his own sect, meaning that every person sees God in a different way.
You also ask if you are totally free to do what you want to do. What do you mean by freedom? If you mean freedom of the senses, no. My guru used to say that what we want is freedom from the senses, not freedom of the senses. Again, Krishna says in the Gita (XVI. 23-24.):
He who discards the injunctions of the scriptures and acts upon the impulse of desire attains neither perfection nor happiness nor the Supreme Goal. Therefore let the scriptures be your authority in determining what ought to be done and what ought not to be done. Having learnt the injunctions of the scriptures, you should do your work in the world.
The scriptures, the Vedas, are a guide as to how to live. So you are not free to do whatever you want under the shadow of Hinduism.
Ramakishna Paramahamsa said to go out and mix with others, say yea to all, but in the evening go to your own room. In other words, mingle with others, read about other religions, but in your heart worship your own Ishta and follow the guide of the scriptures.