1. In the verses, can you spot another compound (besides ‘किंसखा’) which is constructed using the सूत्रम् 2-1-64 किं क्षेपे?
Answer: The compound किंप्रभुः (पुंलिङ्ग-प्रातिपदिकम् ‘किंप्रभु’, प्रथमा-एकवचनम्) is also constructed using the सूत्रम् 2-1-64 किं क्षेपे।

कुत्सितः प्रभुः = किंप्रभुः/किम्प्रभुः – A bad master.

अलौकिक-विग्रह: –
किम् सुँ + प्रभु सुँ । By 2-1-64 किं क्षेपे – A सुबन्तं (ending in a सुँप् affix) पदम् which is composed by adding a सुँप् affix to ‘किम्’ when indicating censure compounds with another सुबन्तं (ending in a सुँप् affix) पदम् – provided both the सुबन्त-पदे refer to the same item – and the resulting compound is a तत्पुरुष:।
Note: This सूत्रम् prescribes a नित्य-समास: because in order to convey the meaning of क्षेपे (censure) the लौकिक-विग्रह: has to be constructed using words other than those present in the compound.

By 1-2-43 प्रथमानिर्दिष्टं समास उपसर्जनम् – the term ‘किम् सुँ’ gets the designation उपसर्जनम् because in the सूत्रम् 2-1-64 (which prescribes the compounding) the term किम् ends in the nominative case. Hence ‘किम् सुँ’ is placed in the prior position in the compound as per the सूत्रम् 2-2-30 उपसर्जनं पूर्वम्‌।

Note: ‘किम् सुँ + प्रभु सुँ’ gets the designation प्रातिपदिकम्‌ by 1-2-46 कृत्तद्धितसमासाश्च। This allows 2-4-71 to apply in the next step.
= किम् + प्रभु । By 2-4-71 सुपो धातुप्रातिपदिकयोः।
= किं + प्रभु । By 8-3-23 मोऽनुस्वारः।
= किंप्रभु/किम्प्रभु । By 8-4-59 वा पदान्तस्य।

As per the सूत्रम् 2-4-26 परवल्लिङ्गं द्वन्द्वतत्पुरुषयोः, the compound प्रातिपदिकम् ‘किंप्रभु/किम्प्रभु’ is masculine since the latter member ‘प्रभु’ of the compound is masculine. The compound declines like ‘गुरु’-शब्द:।

2. Commenting on the सूत्रम् 2-1-64 किं क्षेपे the तत्त्वबोधिनी says – क्षेपे किम्? को राजा पाटलिपुत्रे। Please explain.
Answer: The सूत्रम् 2-1-64 किं क्षेपे says – A सुबन्तं (ending in a सुँप् affix) पदम् which is composed by adding a सुँप् affix to ‘किम्’ when indicating censure compounds with another सुबन्तं (ending in a सुँप् affix) पदम् – provided both the सुबन्त-पदे refer to the same item – and the resulting compound is a तत्पुरुष:।
In order to understand the importance of the condition क्षेपे, consider the example – को राजा पाटलिपुत्रे (who is the King in Pāṭaliputra). Here the intention is not to blame/censure the King. Therefore the सूत्रम् 2-1-64 किं क्षेपे cannot be used to form a compound between ‘किम्’ and ‘राजन्’ here.

3. Which सूत्रम् prescribes the seventh case affix in the forms नृपेषु, अमात्येषु and the corresponding adjective अनुकूलेषु?
Answer: The सूत्रम् 2-3-37 यस्य च भावेन भावलक्षणम्‌ prescribes the seventh case affix in the forms नृपेषु (पुंलिङ्ग-प्रातिपदिकम् ‘नृप’, सप्तमी-बहुवचनम्) and अमात्येषु (पुंलिङ्ग-प्रातिपदिकम् ‘अमात्य’, सप्तमी-बहुवचनम्) as well as the corresponding adjective अनुकूलेषु (प्रातिपदिकम् ‘अनुकूल’, पुंलिङ्गे सप्तमी-बहुवचनम्)।

As per the सूत्रम् 2-3-37 यस्य च भावेन भावलक्षणम्‌ – A seventh case affix (‘ङि’, ‘ओस्’, ‘सुप्’) is used following a प्रातिपदिकम् (nominal stem) which denotes the one (agent/object) whose action (the timing of which is known) gives an indication of (the timing of) another action.
Note: In the present example, the action of ‘(being) mutually well-disposed’ (expressed by अनुकूलेषु (सत्सु)) performed by the agent ‘नृप’ (expressed by नृपेषु) and ‘अमात्य’ (expressed by अमात्येषु) gives an indication of the timing of another action which is that of ‘taking delight’ (expressed by रतिं कुर्वते) performed by the agent सर्वसंपदः। Hence as per the सूत्रम् 2-3-37 यस्य च भावेन भावलक्षणम्‌, ‘नृप’ and ‘अमात्य’ – which denote the agents of the indicating action of ‘(being) mutually well-disposed’ – take a seventh case affix.
Note: The action (लक्षण-क्रिया) in the absolute clause is generally expressed by using a participle ending in a कृत् affix. This participle (implied to be ‘सत्’) – being in grammatical agreement with the प्रातिपदिकम् (the subject ‘नृप’/‘अमात्य’) which denotes the agent/object of the action – also takes the seventh case affix to give the form सत्सु।

4. Where does the सूत्रम् 1-4-29 आख्यातोपयोगे find application in the verses?
Answer: The सूत्रम् 1-4-29 आख्यातोपयोगे finds application in the form हितात् (प्रातिपदिकम् ‘हित’, पुंलिङ्गे पञ्चमी-एकवचनम्)।

As per the सूत्रम् 1-4-29 आख्यातोपयोगे – The कारकम् (participant in the action) which denotes a teacher/instructor (in the present example ’हित’ – ‘well-wisher/counsellor’) from whom a student formally (observing the proper rules of conduct) receives knowledge is designated as अपादानम्। And therefore ‘हित’ takes a fifth case affix (to give the form हितात्) as per the सूत्रम् 2-3-28 अपादाने पञ्चमी – A fifth case affix (‘ङसिँ’, ‘भ्याम्’, ‘भ्यस्’) is used to denote the अपादानम् (that from which detachment/ablation takes place) provided it has not been expressed otherwise.

5. Which कृत् affix is used to derive the form अधिपम् (प्रातिपदिकम् ‘अधिप’, पुंलिङ्गे द्वितीया-एकवचनम्)?
Answer: The कृत् affix ‘क’ is used to derive the प्रातिपदिकम् ‘अधिप’ – derived from verbal root √पा (पा रक्षणे २. ५१).
अधिपातीति अधिपः।

Please see answer to question 4 in the following comment for derivation of the form ‘अधिप’ – http://avg-sanskrit.org/2013/04/01/रणे-mls/#comment-19305

6. How would you say this in Sanskrit?
“A contemptible king is one who does not protect (his) subjects.” Construct a कर्मधारय: compound for ‘contemptible king’ = कुत्सितो राजा।
Answer: यः राजा स्वप्रजाः न रक्षति सः किंराजा भवति = यो राजा स्वप्रजा न रक्षति स किंराजा भवति।

Advanced question:
1. How can the use of a आत्मनेपदम् affix in the form संशृणुते be justified?
Answer: The form संशृणुते is derived from the verbal root √श्रु (श्रु श्रवणे १. १०९२) as follows –

The विवक्षा is लँट्, कर्तरि प्रयोग:, प्रथम-पुरुषः, एकवचनम्।
श्रु + लँट् । By 3-2-123 वर्तमाने लट्।
= श्रु + ल् । अनुबन्ध-लोपः by 1-3-2 उपदेशेऽजनुनासिक इत्, 1-3-3 हलन्त्यम्, 1-3-9 तस्य लोपः।
= श्रु + त । By 3-4-78 तिप्तस्झिसिप्थस्थमिब्वस्मस्तातांझथासाथांध्वमिड्वहिमहिङ्। As per 1-3-29 समो गम्यृच्छिभ्याम् – When preceded by the उपसर्गः ‘सम्’ and when used intransitively, the verbal root √गम् (गमॢँ गतौ १. ११३७) or √ऋच्छ् (ऋछँ गतीन्द्रियप्रलयमूर्तिभावेषु ६. १६) takes a आत्मनेपदम् affix (and not the default परस्मैपदम् by 1-3-78 शेषात् कर्तरि परस्मैपदम्।) Note: The काशिका reads the सूत्रम् 1-3-29 as समो गम्यृच्छिप्रच्छिस्वरत्यर्तिश्रुविदिभ्यः, while the सिद्धान्त-कौमुदी lists a वार्तिकम् – अर्तिश्रुदृशिभ्यश्चेति वक्तव्यम्। Thus the application of the सूत्रम् 1-3-29 is not limited to the verbal roots √गम् (गमॢँ गतौ १. ११३७) and √ऋच्छ् (ऋछँ गतीन्द्रियप्रलयमूर्तिभावेषु ६. १६) but is extended to the verbal roots श्रु (श्रु श्रवणे १. १०९२) etc.
Note: The application of the above सूत्रम्/वार्तिकम् requires that the verbal root be used intransitively. And as explained in the commentary – अकर्मकत्वं वैवक्षिकम् – the intransitivity of the verbal root depends on whether the speaker/author desires to express the object. So even though the verbal root √श्रु (श्रु श्रवणे १. १०९२) is capable of taking an object, in the present example no object has been expressed and therefore the verbal root √श्रु (श्रु श्रवणे १. १०९२) is used intransitively here. This allows the application of the सूत्रम् 1-3-29.
= श्रु + ते । By 3-4-79 टित आत्मनेपदानां टेरे।
= शृ + श्नु + ते । By 3-1-74 श्रुवः शृ च – The affix ‘श्नु’ is placed after the verbal root √श्रु (श्रु श्रवणे १. १०९२), when followed by a सार्वधातुकम् affix that is used signifying the agent. Simultaneously, ’श्रु’ takes the substitution ’शृ’। The affix ‘श्नु’ which is a शित् (has the letter ’श्’ as a इत्) as well as the affix ’ते’ gets सार्वधातुक-सञ्ज्ञा by 3-4-113 तिङ्शित्सार्वधातुकम्।
= शृ + नु + ते । अनुबन्ध-लोपः by 1-3-8 लशक्वतद्धिते , 1-3-9 तस्य लोपः ।
Note: The affixes ’नु’ and ‘ते’ are ङिद्वत् (behave as if they have the letter ‘ङ्’ as a इत्) by 1-2-4 सार्वधातुकमपित्। Therefore 1-1-5 क्क्ङिति च prevents 7-3-84 from performing the गुण: substitution for the letter ‘ऋ’ of ’शृ’ as well as the letter ‘उ’ of ’नु’।
= शृणुते । By वार्त्तिकम् (under 8-4-1) – ऋवर्णान्नस्य णत्वं वाच्यम्।

’सम्’ is the उपसर्गः (ref. 1-4-59 उपसर्गाः क्रियायोगे, 1-4-80 ते प्राग्धातोः।)
सम् + शृणुते = संशृणुते । By 8-3-23 मोऽनुस्वारः।

Easy question:
1. Where has the सूत्रम् 7-1-5 आत्मनेपदेष्वनतः been used in the verses?
Answer: The सूत्रम् 7-1-5 आत्मनेपदेष्वनतः has been used in the form कुर्वते – derived from the verbal root √कृ (डुकृञ् करणे ८. १०).

Please see answer to question 4 in the following comment for derivation of the form कुर्वते – https://avg-sanskrit.org/2011/11/07/कुर्वन्ति-3ap-लँट्/#comment-1666