1. Why doesn’t the ending letter ‘न्’ of the substitute ‘ईन्’ (used in step 7) get the designation इत् (as per the सूत्रम् 1-3-3 हलन्त्यम्)? In answer to this the तत्त्वबोधिनी says आयनीनोर्नकारस्य नेत्त्वम्, फिनो नित्करणसामर्थ्यात्। Please explain. Note: ‘फिन्’ is a तद्धित: affix prescribed by the सूत्रम् 4-1-160 प्राचामवृद्धात्‌ फिन् बहुलम्‌।
Answer: The ending letter ‘न्’ of the तद्धित: affix ‘फिन्’ (prescribed by the सूत्रम् 4-1-160 प्राचामवृद्धात्‌ फिन् बहुलम्‌) is a इत् by 1-3-3 हलन्त्यम्। (The purpose of the letter ‘न्’ being a इत् in the affix ‘फिन्’ is to prescribe a particular स्वरः – intonation).
There would be no purpose served by having the ending letter ‘न्’ of the affix ‘फिन्’ as a इत् if the ending letter ‘न्’ of the substitute ‘आयन्’ (in place of the letter ‘फ्’) were to be a इत् because in that case ‘फिन्’ would inherit the property of being a नित् (having the letter ‘न्’ as a इत्) from the substitute ‘आयन्’ already. Hence the fact that the affix ‘फिन्’ has been specifically made a नित् tells us that the ending letter ‘न्’ of the substitute ‘आयन्’ is not a इत्। And based on the association of ‘ईन्’ with ‘आयन्’ (in the सूत्रम् 7-1-2 आयनेयीनीयियः फढखछघां प्रत्ययादीना) we extend this logic to apply equally to ‘ईन्’ as well and conclude that the ending letter ‘न्’ of ‘ईन्’ is also not a इत्।

2. Where has the सूत्रम् 8-2-45 ओदितश्च been used in the verses?
Answer: The सूत्रम् 8-2-45 ओदितश्च has been used in the form हीनाम् (स्त्रीलिङ्ग-प्रातिपदिकम् ‘हीना’, द्वितीय-एकवचनम्) – derived from the verbal root √हा (ओँहाक् त्यागे ३. ९).

Please see answer to question 4 in the following comment for derivation of the स्त्रीलिङ्ग-प्रातिपदिकम् ‘हीना’ – https://avg-sanskrit.org/2014/11/27/मानुष्यम्-nas/#comment-3513

3. From which verbal root is the participle ‘ईप्सित’ (used in the compound ‘लीलावतारेप्सितजन्म’ in the verses) derived?
Answer: The participle ‘ईप्सित’ is derived from the verbal root √आप् (आपॢँ व्याप्तौ ५. १६).

Please see the following post for derivation of the participle form ‘ईप्सित’ –
http://avg-sanskrit.org/2012/11/19/ईप्सितम्-nns

4. What is the विग्रह-वाक्यम् (explanatory sentence) of the अव्ययीभाव: compound प्रतिक्षणम् used in the commentary?
Answer: The विग्रह-वाक्यम् of the अव्ययीभाव: compound प्रतिक्षणम् is
क्षणे क्षणे = प्रतिक्षणम् = at moment after moment = at each moment

अलौकिक-विग्रह: –
क्षण ङि + प्रति । By 2-1-6 अव्ययं विभक्तिसमीपसमृद्धिव्यृद्ध्यर्थाभावात्ययासम्प्रतिशब्दप्रादुर्भावपश्चाद्यथानुपूर्व्ययौगपद्यसादृश्यसम्पत्तिसाकल्यान्तवचनेषु – A अव्ययम्‌ (indeclinable) used in any one of the following meanings invariably compounds with a (syntactically related) term ending in a सुँप् affix to yield a अव्ययीभाव: compound –
(i) विभक्ति: – a case affix
(ii) समीपम्‌ – close by
(iii) समृद्धि: (ऋद्धेराधिक्यम्‌) – prosperity
(iv) व्यृद्धि: (विगता ऋद्धि:) – adversity
(v) अर्थाभाव: – absence of something
(vi) अत्यय: (ध्वंस:) – disappearance (passing away)
(vii) असम्प्रति – presently inappropriate
(viii) शब्दप्रादुर्भाव: – manifestation of a sound
(ix) पश्चाद् – following
(x) यथा (योग्यतावीप्सापदार्थानतिवृत्तिसादृश्यानि यथार्था:) – appropriateness, repetition, non-transgression of something, similarity
(xi) आनुपूर्व्यम्‌ – in orderly succession
(xii) यौगपद्यम्‌ – simultaneity
(xiii) सादृश्यम्‌ – similarity/resemblance. Note: यथार्थत्वेनैव सिद्धे पुन: सादृश्यग्रहणं गुणभूतेऽपि सादृश्ये यथा स्यादित्येवमर्थम्‌ – सादृश्यम्‌ is mentioned here again (even though it is already given as one of the meanings of यथा in (x) above) in order to allow compounding even when सादृश्यम्‌ is used in a secondary (adjectival) sense
(xiv) सम्पत्ति: (अनुरूप आत्मभाव:) – befitting state
(xv) साकल्यम्‌ – totality/completeness
(xvi) अन्त: – termination/end
Note: The term ‘वचन’ used at the end of the compound विभक्ति……वचनेषु connects with each one of the prior terms ‘विभक्ति’ etc in the compound.
= प्रति + क्षण ङि । By 1-2-43 प्रथमानिर्दिष्टं समास उपसर्जनम् – A term denoted by a word ending in a nominative case in a सूत्रम् which prescribes a compound gets the designation ‘उपसर्जन’। Here the term ‘अव्ययम्’ in the सूत्रम् 2-1-6 ends in the nominative case. Therefore the अव्ययम् ‘प्रति’ gets the designation ‘उपसर्जन’ by 1-2-43. Hence ‘प्रति’ is placed in the prior position in the compound as per the सूत्रम् 2-2-30 उपसर्जनं पूर्वम्‌।
Note: ‘प्रति + क्षण ङि’ gets the designation प्रातिपदिकम्‌ by 1-2-46 कृत्तद्धितसमासाश्च। This allows 2-4-71 to apply in the next step.
= प्रति + क्षण । By 2-4-71 सुपो धातुप्रातिपदिकयोः।
= प्रतिक्षण ।

प्रतिक्षण + सुँ (default) । By 4-1-2 स्वौजसमौट्छष्टाभ्याम्भिस्ङेभ्याम्भ्यस्ङसिभ्याम्भ्यस्ङसोसाम्ङ्योस्सुप्‌।
= प्रतिक्षण + अम् । By 2-4-83 नाव्ययीभावादतोऽम्त्वपञ्चम्याः – This सूत्रम् has two parts – (a) नाव्ययीभावादत: – following a अव्ययीभावः compound ending (ref. 1-1-72) in the letter ‘अ’ a सुँप् affix does not take the लुक् elision (which would have been done by 2-4-82 अव्ययादाप्सुपः) and (b) अम्त्वपञ्चम्याः – following a अव्ययीभावः compound ending (ref. 1-1-72) in the letter ‘अ’ a सुँप् affix – other than a fifth case affix – is substituted by अम्।
1-3-4 न विभक्तौ तुस्माः prevents the ending letter ‘म्’ of the affix ‘अम्’ from getting इत्-सञ्ज्ञा।
= प्रतिक्षणम् । By 6-1-107 अमि पूर्वः।

5. Which सूत्रम् prescribes the affix ‘ण्वुल्’ used in the form शोधकम् (प्रातिपदिकम् ‘शोधक’, नपुंसकलिङ्गे प्रथमा-एकवचनम्) in the commentary?
Answer: The सूत्रम् 3-1-133 ण्वुल्तृचौ prescribes the affix ‘ण्वुल्’ used in the form शोधकम् – derived from the verbal root √शुध् (शुधँ शौचे ४.८८) as follows –

शुध् + ण्वुल् । By 3-1-133 ण्वुल्तृचौ – The affixes ‘ण्वुल्’ and ‘तृच्’ may be used after a verbal root. Note: As per 3-4-67 कर्तरि कृत्‌, the affixes ‘ण्वुल्’ and ‘तृच्’ are used in the sense of the agent of the action.
= शुध् + वु । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम्, 1-3-7 चुटू, 1-3-9 तस्य लोपः।
= शुध् + अक । By 7-1-1 युवोरनाकौ, 1-1-55 अनेकाल्शित्सर्वस्य।
= शोध् + अक । By 7-3-86 पुगन्तलघूपधस्य च।
= शोधक । ‘शोधक’ gets प्रातिपदिक-सञ्ज्ञा by 1-2-46 कृत्तद्धितसमासाश्च।

6. How would you say this in Sanskrit?
“In childhood I was not independent but now I am.” Paraphrase to “In childhood I was dependent on another but now I am self-dependent.” Use the neuter noun ‘शैशव’ for ‘childhood.’ Form a compound for ‘dependent on another’ and ‘self-dependent (dependent on oneself.)’
Answer: शैशवे पराधीनः आसम् साम्प्रतम् तु स्वाधीनः अस्मि = शैशवे पराधीन आसं साम्प्रतं तु स्वाधीनोऽस्मि।

Easy questions:
1. Which सूत्रम् prescribes the substitution ‘इ’ in the form बिभृयात्?
Answer: The सूत्रम् 7-4-76 भृञामित्‌ prescribes the substitution ‘इ’ in the form बिभृयात् derived from √भृ ( डुभृञ् धारणपोषणयोः ३.६).

Please see answer to question 4 in the following comment for derivation of the form बिभृयात् – https://avg-sanskrit.org/2012/10/01/बुधः-mns/#comment-4877

2. Can you spot the affix ‘श्नु’ in the commentary?
Answer: The affix ‘श्नु’ occurs in the form विवृणोति – derived from the verbal root √वृ (वृञ् वरणे ५. ८).

The विवक्षा is लँट्, कर्तरि प्रयोग:, प्रथम-पुरुषः, एकवचनम्।
वृ + लँट् । By 3-2-123 वर्तमाने लट्।
= वृ + ल् । अनुबन्ध-लोपः by 1-3-2 उपदेशेऽजनुनासिक इत्, 1-3-3 हलन्त्यम्, 1-3-9 तस्य लोपः।
= वृ + तिप् । By 3-4-78 तिप्तस्झिसिप्थस्थमिब्वस्मस्तातांझथासाथांध्वमिड्वहिमहिङ्, 1-3-78 शेषात् कर्तरि परस्मैपदम्।
Note: The affix ‘तिप्’ has the सार्वधातुक-सञ्ज्ञा by 3-4-113 तिङ्शित्सार्वधातुकम्। This allows 3-1-73 to apply below.
= वृ + ति । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम्, 1-3-9 तस्य लोपः।
= वृ + श्नु + ति । By 3-1-73 स्वादिभ्यः श्नुः – The affix ‘श्नु’ is placed after the verbal roots of the स्वादि-गणः, when followed by a सार्वधातुकम् affix that is used signifying the agent. This सूत्रम् is a अपवाद: (exception) to 3-1-68 कर्तरि शप्‌ ।
= वृ + नु + ति । अनुबन्ध-लोपः by 1-3-8 लशक्वतद्धिते , 1-3-9 तस्य लोपः।
Note: By 1-2-4 सार्वधातुकमपित्, the affix ‘नु’ becomes ङिद्वत् (behaves like having the letter ‘ङ्’ as a इत्)। Hence 1-1-5 क्क्ङिति च prevents the गुणादेशः for the letter ‘ऋ’ (of the अङ्गम् ‘वृ’) which would have been done by 7-3-84 सार्वधातुकार्धधातुकयोः।
= वृनोति । By 7-3-84 सार्वधातुकार्धधातुकयोः।
= वृणोति । By 8-4-2 अट्कुप्वाङ्नुम्व्यवायेऽपि, वार्तिकम् – ऋवर्णान्नस्य णत्वं वाच्यम्।

‘वि’ is the उपसर्ग: (ref. 1-4-59 उपसर्गाः क्रियायोगे, 1-4-80 ते प्राग्धातोः।)
वि + वृणोति = विवृणोति । By 6-1-77 इको यणचि।