In Adhyaya 5 Pada 2 Sutra 1 of the Nyaya Sutras, Gautama lists the 22 argumentative moves that cause you to lose a debate, known as Nigrahasthanas or Clinchers:
pratijñāhāniḥ pratijñāntaraṃ pratijñāvirodhaḥ pratijñāsaṃnyāso hetvantaramarthāntaraṃ nirarthakam avijñātārtham apārthakam aprāptakālaṃ nyūnamadhikaṃ punaruktam ananubhāṣaṇam ajñānam apratibhā ...
The Nyaya Sutras accept the existence of God.. Here is what Gautama says in Adhyaya 4 Pada 1 of the Nyaya Sutras (from Ganganatha Jha's translation):
īśvaraḥ kāraṇaṁ puruṣakarmāphalyadarśanāt
God is the cause; because we find fruitlessness in the actions of Men.
na puruṣakarmābhāve phalāniṣpatteḥ
It is not so; because as a matter of fact, no fruit ...
I know of six commentaries on Gautama's Nyaya Sutras:
Vatsyayana's Nyaya Sutra Bhashya, which you can read here.
Uddyotakara's Vartika on Vatsyayana's Bhashya, which you can read in four volumes here, here, here, and here.
Vachaspati Mishra's Tatparya Tika on Uddyotaraka's Vartika, which isn't available in English, but is available in Sanskrit here.
I know about two English translations with commentaries which are freely available online. I think you will get it in archive.org
The aphorisms of the Nyaya Philosophy by Goutama with illustrative extracts from the commentary by Vishwantha (in Sanskrit and English), Allahabad, 1850.
The sacred books of the Hindus Vol VIII: The Nyaya sutras of Gotama. ...
In Nyaya darshan, ATma is vibhu, that is it is of infinite dimension and pervasive, not limited. So it cannot have samyoga (in nyaya, there are two relationships samyoga=conjunction, and samvaya=inherent) with another pervasive substance. However, atma -manah samyoga is necessary for knowledge. Thus mind has to be of lesser dimension than vibhu. It cannot ...
In his translation of this verse, Swami Maddhavananda writes (Bhasa Pariccheda with Siddhanta-Muktavali by Visvanatha-Nyaya-Pancanana, translation by Swami Madhavananda):
85. The instrument of the cognition of pleasure etc. is called the mind. In this system it is considered to be atomic, since states of consciousness are not simultaneous.
[and at ...
There have been a few commentaries on the Gautama Nyaya Sutras. The names are given in The Nyaya sutras of Gotama. Translated by Mahamahopadhyay Satishchandra Vidyabhushana.
The book lists 15 commentaries on the Nyaya Sutras.
Nyaya Bhashya by Vatsayana otherwise known as Pakshila swami.
Nyaya Vartika by Udyotakara
Nyaya Vartika Tatparya Tika by ...