Your questions:
how does an unconscious thing listens to my someones chanting? Are Gods conscious beings who can hear someone's prayer?
If you believe in the Scriptures, God is Consciousness and bliss Himself- -Sat-Chit-Ananda Swarupa.
Mandukyopanishad (6)says:
"Esha Sarveswara esha Sarvajna eso anntaryami" meaning that God is All-knowing and Knows the minds of all.
Gita (18/61)also says:
"Iswarah sarvabhutanaam hriddeshe arjuna tisthati" meaning God resides in the heart of all beings.
So God is always conscious of everything and watching, listening and knowing everything.
What are the mantras? According to our scriptures, matra is the "Vaikhari" form, that is one form, of God. So Mantras are known as the Vangmoyee tanu (form expressed as words of God. So NO ONE EXCEPT SHIVA CAN CREATE MANTRAS. (Reference: M-karbaba, Omkarnath Rachanavali, chapter 7). So, Kularnavatantra (17/34) says:
japa destoys sins of thousand previous births and reveals God.
You wrote you feel peace inside.
This is supported by the vachanas of many scriptures.Shiva-Purana says:
"Tamasontarvahirnaasho prashantih parigiyate".
ie When our inner darkness is removed, we feel peace of mind.(Dikshasaara, page 225)
In manrayogasamhita, Vrihannilatantra,Gandharvatantra, Mantramahodadhi and Kularnavatantra unianimously declares :
"Anandashruni pulako" ( tears of joy and feeling bliss), "manah prasadah santoshah ( peace of mind and bliss) are effect of chanting mantra correctly ( Deektshasaara, page 263).
- You asked : What is the logic or its just the belief? Yes, there is. But spiritulal logic. That one has to understand and experience yourself. We read in biographies of so many saints all these to be true.
But as Rickross righly said, Guru is needed for proper guidance in mantrasadhana.There are other important indications like jyoti, naada, visions etc that indicate that you are on the right track.