1. Where has the सूत्रम् 2-2-6 नञ्‌ (used in step 2) been used for the first time in Chapter Sixteen of the गीता?
Answer: The सूत्रम् 2-2-6 नञ्‌ has been used for the first time in Chapter Sixteen of the गीता in the form अभयम् (नपुंसकलिङ्ग-प्रातिपदिकम् ‘अभय’, प्रथमा-एकवचनम्)।

अभयं सत्त्वसंशुद्धिर्ज्ञानयोगव्यवस्थितिः |
दानं दमश्च यज्ञश्च स्वाध्यायस्तप आर्जवम्‌ || 16-1||

न भयम् = अभयम् – absence of fear
In the above compound, the particle नञ्‌ conveys the sense of अभाव: – absence of that which is being negated.

The derivation of the compound प्रातिपदिकम् ‘अभय’ is similar to the derivation of the compound प्रातिपदिकम् ‘असंशय’ as shown in the post.
As per the सूत्रम् 2-4-26 परवल्लिङ्गं द्वन्द्वतत्पुरुषयोः, the compound प्रातिपदिकम् ‘अभय’ is neuter since the latter member ‘भय’ of the compound is neuter in gender. The compound declines like वन-शब्द:। प्रथमा-एकवचनम् is अभयम्।

2. Can you spot two other (besides असंशय:) नञ्-तत्पुरुष: compounds in the verses?
Answer: The compounds अभक्ताय (प्रातिपदिकम् ‘अभक्त’, पुंलिङ्गे चतुर्थी-एकवचनम्) and अशुश्रूषवे (प्रातिपदिकम् ‘अशुश्रूषु’, पुंलिङ्गे चतुर्थी-एकवचनम्) are also नञ्-तत्पुरुष: compounds.

न भक्तः = अभक्तः – Non-devotee
न शुश्रूषुः = अशुश्रूषुः – Not desiring to listen
In the above two compounds, the particle नञ्‌ conveys the sense of विरोध: – opposite of that which is being negated.

The derivation of the compound प्रातिपदिकम् ‘अभक्त’ as well as ‘अशुश्रूषु’ is similar to the derivation of the compound प्रातिपदिकम् ‘अपर्याप्त’ shown in answer to question 1 in the following comment – https://avg-sanskrit.org/2015/08/10/अब्राह्मणः-mns/#comment-35496

As per the सूत्रम् 2-4-26 परवल्लिङ्गं द्वन्द्वतत्पुरुषयोः, the compounds ‘अभक्त’ and ‘अशुश्रूषु’ are adjectives, since the latter members ‘भक्त’ and ‘शुश्रूषु’ of the compounds are adjectives. Here they are used in the masculine gender.

3. In which word(s) in the verses has the सूत्रम् 2-1-49 पूर्वकालैकसर्वजरत्पुराणनवकेवलाः समानाधिकरणेन been used?
Answer: The सूत्रम् 2-1-49 पूर्वकालैकसर्वजरत्पुराणनवकेवलाः समानाधिकरणेन has been used in the forms सर्वधर्मान् (पुंलिङ्ग-प्रातिपदिकम् ‘सर्वधर्म’, द्वितीया-बहुवचनम्) and सर्वपापेभ्यः (नपुंसकलिङ्ग-प्रातिपदिकम् ‘सर्वपाप’, पञ्चमी-बहुवचनम्)।

सर्वाणि च तानि पापानि = सर्वपापानि – all sins
सर्वे च ते धर्माः = सर्वधर्माः – all duties

The derivation of the compound प्रातिपदिकम् ‘सर्वधर्म’ as well as ‘सर्वपाप’ is similar to the derivation of the compound प्रातिपदिकम् ‘सर्वसत्त्व’ as shown in answer to question 3 in the following comment – https://avg-sanskrit.org/2015/05/21/सप्तर्षिभिः-mip/#comment-35293

As per the सूत्रम् 2-4-26 परवल्लिङ्गं द्वन्द्वतत्पुरुषयोः, the compound प्रातिपदिकम् ‘सर्वधर्म’ is masculine since the latter member ‘धर्म’ of the compound is masculine and the compound प्रातिपदिकम् ‘सर्वपाप’ is neuter since the latter member ‘पाप’ of the compound is neuter.

4. Which कृत्य-प्रत्यय: is used to derive the प्रातिपदिकम् ‘वाच्य’ (used in the form वाच्यम् (नपुंसकलिङ्गे, प्रथमा-एकवचनम्) in the verses)?
Answer: The कृत्य-प्रत्यय: ‘ण्यत्’ is used to derive the प्रातिपदिकम् ‘वाच्य’।

Please see the following post for the derivation of the प्रातिपदिकम् ‘वाच्य’ –
http://avg-sanskrit.org/2012/09/17/वाच्यः-mns/

5. What kind of compound is दृढविश्वासेन (पुंलिङ्ग-प्रातिपदिकम् ‘दृढविश्वास’, तृतीया-एकवचनम्) used in the commentary?
i. अव्ययीभाव:
ii. नञ्-तत्पुरुष:
iii. कर्मधारय:
iv. षष्ठी-तत्पुरुष:
Answer: It is a कर्मधारयः compound.

दृढश्चासौ विश्वासः = दृढविश्वासः – firm faith

अलौकिक-विग्रह: –
दृढ सुँ + विश्वास सुँ । By 2-1-57 विशेषणं विशेष्येण बहुलम्‌।
By 1-2-43 प्रथमानिर्दिष्टं समास उपसर्जनम् – the adjective ’दृढ सुँ’ gets the designation उपसर्जनम् because in the सूत्रम् 2-1-57 (which prescribes the compounding) the term विशेषणम्‌ ends in the nominative case. Hence ‘दृढ सुँ’ is placed in the prior position in the compound as per the सूत्रम् 2-2-30 उपसर्जनं पूर्वम्‌।
Note: ‘दृढ सुँ + विश्वास सुँ’ gets the designation प्रातिपदिकम्‌ by 1-2-46 कृत्तद्धितसमासाश्च। This allows 2-4-71 to apply in the next step.
= दृढ + विश्वास । By 2-4-71 सुपो धातुप्रातिपदिकयोः।
= दृढविश्वास ।
Note: As per the सूत्रम् 2-4-26 परवल्लिङ्गं द्वन्द्वतत्पुरुषयोः, the compound प्रातिपदिकम् ‘दृढविश्वास’ is masculine since the latter member ‘विश्वास’ of the compound is masculine. It declines like राम-शब्दः। तृतीया-एकवचनम् is दृढविश्वासेन।

6. How would you say this in Sanskrit?
“It’s definitely going to rain tomorrow.” Paraphrase to “There will be rain tomorrow. (There is) no doubt.” Use the feminine प्रातिपदिकम् ‘वर्षा’ for ‘rain.’
श्वः वर्षा भविष्यति असंशयः = श्वो वर्षा भविष्यत्यसंशयः।

Easy questions:
1. Where has the सूत्रम् 3-1-27 कण्ड्वादिभ्यो यक् been used in the verses?
Answer: The सूत्रम् 3-1-27 कण्ड्वादिभ्यो यक् has been used in the verses in the form अभ्यसूयति – derived from the verbal root √असु (असु उपतापे, कण्ड्वादि-गणः)।

Please see answer to question 1 in the following comment for the derivation of the form अभ्यसूयति – http://avg-sanskrit.org/2012/08/13/कण्डूयन्ते-3ap-लँट्/#comment-4189

2. Can you spot the affix णिच् in the verses?
Answer: The affix ‘णिच्’ occurs in the word मोक्षयिष्यामि – derived from the verbal root √मोक्ष् (मोक्षँ असने १०. २५६).

Please see answer to question 1 in the following comment for derivation of the form मोक्षयिष्यामि – https://avg-sanskrit.org/2012/03/08/जनयिष्यथ-2ap-लृँट्/#comment-3453