1. What are the three alternate forms for the compound ‘शङ्खतूर्यमृदङ्ग’?
Answer: As per बहुष्वनियम: – when more than one member of the compound has the least number of syllables (vowels), any of these members may be placed in the prior position and the remaining members of the compound may be placed in any order. Therefore we can either place ‘शङ्ख जस्’ or ‘तूर्य जस्’ in the prior position followed by the remaining two in any order.

Hence the alternate forms for the compound ‘शङ्खतूर्यमृदङ्ग’ are –
‘शङ्खमृदङ्गतूर्य’, ‘तूर्यशङ्खमृदङ्ग’ and ‘तूर्यमृदङ्गशङ्ख’।

2. Which compound used in the verses is a नञ्-तत्पुरुष: compound?
Answer: The compound अवितथैः (प्रातिपदिकम् ’अवितथ’, पुंलिङ्गे तृतीया-बहुवचनम्) is a नञ्-तत्पुरुष: compound.

The लौकिक-विग्रहः is –
न वितथ: = अवितथ: – not false

Here the negation particle नञ्‌ conveys the sense of विरोध: – opposite of that which is being negated.
The derivation of the compound प्रातिपदिकम् ‘अवितथ’ 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 compound प्रातिपदिकम् ‘अवितथ’ is an adjective since the latter member ‘वितथ’ of the compound is an adjective. Since the compound is qualifying the masculine noun ’मन्त्र’, it is used in the masculine here. The compound declines like राम-शब्द:। तृतीया-बहुवचनम् is अवितथैः।

3. Why is the compound सस्त्रीणाम् used in the verses a आर्षप्रयोगः (irregular grammatical usage?)
Answer: The compound सस्त्रीणाम् used in the verses a आर्षप्रयोगः because the सूत्रम् 5-4-153 नद्‍यृतश्च has not been followed. The grammatically correct form is सस्त्रीकाणाम् (प्रातिपदिकम् ’सस्त्रीक’, पुंलिङ्गे षष्ठी-बहुवचनम्)।

लौकिक-विग्रह: is –
स्त्रीभि: सह (वर्तन्ते देवानुगा:) = सस्त्रीकाः (वर्तन्ते देवानुगा:) – (Gandharvas present) with women (their spouses).
Note: The third case affix used in स्त्रीभि: is as per the सूत्रम् 2-3-19 सहयुक्तेऽप्रधाने।
The derivation of the compound प्रातिपदिकम् ’सस्त्रीक’ is shown in the following post – https://avg-sanskrit.org/2016/01/28/सस्त्रीकाः-mnp/

The gender of a बहुव्रीहि: compound matches that of which it qualifies. In the present example, सस्त्रीकाणाम् is qualifying देवानुगानाम् (गन्धर्वाणाम्।) Hence the compound प्रातिपदिकम् ‘सस्त्रीक’ is used in the masculine gender. It declines like राम-शब्द:। षष्ठी-बहुवचनम् is सस्त्रीकाणाम्।

4. Where has the सूत्रम् 3-2-78 सुप्यजातौ णिनिस्ताच्छील्ये been used in the verses?
Answer: The सूत्रम् 3-2-78 सुप्यजातौ णिनिस्ताच्छील्ये has been used in the verses in the form पुष्पवर्षिणः (प्रातिपदिकम् ’पुष्पवर्षिन्’, पुंलिङ्गे प्रथमा-बहुवचनम्)।

पुष्पाणि वर्षति तच्छीलः = पुष्पवर्षी ।

‘वर्षिन्’ is a कृदन्त-प्रातिपदिकम् (participle form) derived from the verbal root √वृष् (वृषुँ सेचने हिंसासङ्क्लेशनयोश्च १. ८०३).

The (compound) प्रातिपदिकम् ‘पुष्पवर्षिन्’ is derived as follows:
पुष्प + आम् + वृष् + णिनिँ । By 3-2-78 सुप्यजातौ णिनिस्ताच्छील्ये – When in composition with a सुबन्तं पदम् (a पदम् which ends in a सुँप् affix) which does not denote a class/genus, a verbal root may take the affix ‘णिनिँ’ to express the meaning of a habitual/natural action.
Note: In the सूत्रम् 3-2-78, the term सुपि ends in the seventh (locative) case. Hence ‘पुष्प + आम्’ gets the उपपद-सञ्ज्ञा here by 3-1-92 तत्रोपपदं सप्तमीस्थम्‌।
Note: The affix ‘आम्’ is used here as per 2-3-65 कर्तृकर्मणोः कृति। (This is what is called as कृद्योगे षष्ठी)।
= पुष्प + आम् + वृष् + इन् । अनुबन्ध-लोप: by 1-3-2 उपदेशेऽजनुनासिक इत्, 1-3-7 चुटू and 1-3-9 तस्य लोपः।
= पुष्प + आम् + वर्ष् + इन् । By 7-3-86 पुगन्तलघूपधस्य च, 1-1-51 उरण् रपरः।
We form a compound between ’पुष्प + आम्’ (which is the उपपदम्) and ‘वर्षिन्’ by using the सूत्रम् 2-2-19 उपपदमतिङ्। In the compound, ‘पुष्प + आम्’ is placed in the prior position as per 2-2-30 उपसर्जनं पूर्वम्‌। Note: Here ‘पुष्प + आम्’ is the उपपदम् and hence it gets the उपसर्जन-सञ्ज्ञा by 1-2-43 प्रथमानिर्दिष्टं समास उपसर्जनम् – A term denoted by a word (in this case ‘उपपदम्’) ending in a nominative case in a सूत्रम् (in this case 2-2-19 उपपदमतिङ्) which prescribes a compound gets the designation ‘उपसर्जन’।
‘पुष्प + आम् + वर्षिन्’ gets प्रातिपदिक-सञ्ज्ञा by 1-2-46 कृत्तद्धितसमासाश्च। This allows us to apply 2-4-71 in the next step.
= पुष्प + वर्षिन् । By 2-4-71 सुपो धातुप्रातिपदिकयोः।
= पुष्पवर्षिन् ।

The विवक्षा is पुंलिङ्गे, प्रथमा-बहुवचनम्।
पुष्पवर्षिन् + जस् । By 4-1-2 स्वौजसमौट्छष्टाभ्याम्भिस्ङेभ्याम्भ्यस्ङसिँभ्याम्भ्यस्ङसोसाम्ङ्योस्सुप्।
= पुष्पवर्षिन् + अस् । अनुबन्ध-लोपः by 1-3-7 चुटू and 1-3-9 तस्य लोपः। 1-3-4 न विभक्तौ तुस्माः prevents the ending letter ‘स्’ of the affix ‘जस्’ from getting the इत्-सञ्ज्ञा।
= पुष्पवर्षिनः । रुँत्व-विसर्गौ by 8-2-66 ससजुषो रुः and 8-3-15 खरवसानयोर्विसर्जनीयः।
= पुष्पवर्षिणः । By 8-4-2 अट्कुप्वाङ्नुम्व्यवायेऽपि।

5. In which word in the verses has the affix ‘क्विँप्’ been used?
Answer: The affix ‘क्विँप्’ has been used in the form विश्वसृजः (प्रातिपदिकम् ‘विश्वसृज्’, पुंलिङ्गे प्रथमा-बहुवचनम्)।

विश्वं सृजतीति विश्वसृट् – creator of the world

‘सृज्’ is a कृदन्त-प्रातिपदिकम् (participle form) derived from the verbal root √सृज् (सृजँ विसर्गे ४. ७५, ६. १५०). The (compound) प्रातिपदिकम् ‘विश्वसृज्’ is derived as follows:
विश्व + ङस् + सृज् + क्विँप् । By 3-2-76 क्विप् च – (In addition to the affixes mentioned in the सूत्रम् 3-2-74), the affix ‘क्विँप्’ may also be used (following any verbal root with or without the presence of a उपपदम्।)
Note: The term सुपि (which comes as अनुवृत्ति: into the सूत्रम् 3-2-76 क्विप् च from the सूत्रम् 3-2-4 सुपि स्थः) ends in the seventh (locative) case. Hence ‘विश्व + ङस्’ gets the उपपद-सञ्ज्ञा here by 3-1-92 तत्रोपपदं सप्तमीस्थम्‌।
Note: The affix ‘ङस्’ is used here as per 2-3-65 कर्तृकर्मणोः कृति। This is what is called as कृद्योगे षष्ठी।
= विश्व + ङस् + सृज् + व् । अनुबन्ध-लोप: by 1-3-2 उपदेशेऽजनुनासिक इत्, 1-3-3 हलन्त्यम्, 1-3-8 लशक्वतद्धिते and 1-3-9 तस्य लोपः।
= विश्व + ङस् + सृज् । By 6-1-67 वेरपृक्तस्य। As per 1-2-41 अपृक्त एकाल् प्रत्ययः, here the letter ‘व्’ has अपृक्त-सञ्ज्ञा। This allows 6-1-67 to apply.
Note: The affix क्विँप् is a कित् (has the letter ‘क्’ as a इत्)। This enables 1-1-5 क्क्ङिति च to stop 7-3-86 पुगन्तलघूपधस्य च।
We form a compound between ‘विश्व + ङस्’ (which is the उपपदम्) and ‘सृज्’ by using the सूत्रम् 2-2-19 उपपदमतिङ्। In the compound, ‘विश्व + ङस्’ is placed in the prior position as per 2-2-30 उपसर्जनं पूर्वम्‌। Note: Here ‘विश्व + ङस्’ is the उपपदम् and hence it gets the उपसर्जन-सञ्ज्ञा by 1-2-43 प्रथमानिर्दिष्टं समास उपसर्जनम् because in the सूत्रम् 2-2-19 उपपदमतिङ् (which prescribes the compounding) the term उपपदम् ends in the nominative case.
‘विश्व + ङस् + सृज्’ gets प्रातिपदिक-सञ्ज्ञा by 1-2-46 कृत्तद्धितसमासाश्च। This allows us to apply 2-4-71 in the next step.
= विश्व + सृज् । By 2-4-71 सुपो धातुप्रातिपदिकयोः।
= विश्वसृज्।

The विवक्षा is पुंलिङ्गे, प्रथमा-बहुवचनम्। Hence the form is विश्वसृजः।

6. How would you say this in Sanskrit?
“The demons struck the monkeys with swords, spears, and javelins.” Construct a द्वन्द्व: compound for ‘swords, spears and javelins’ = ‘खड्गाश्च शूलाश्च तोमराश्च’। Use the verbal root √तड् (तडँ आघाते १०.६४) for ‘to strike.’
Answer: राक्षसाः खड्गशूलतोमरैः/शूलखड्गतोमरैः/खड्गतोमरशूलैः/शूलतोमरखड्गैः वानरान् ताडयामासु: = राक्षसाः खड्गशूलतोमरैर्/शूलखड्गतोमरैर्/खड्गतोमरशूलैर्/शूलतोमरखड्गैर् वानरान् ताडयामासु:।

Easy questions:
1. Where has the सूत्रम् 2-4-77 गातिस्थाघुपाभूभ्यः सिचः परस्मैपदेषु been used in the verses?
Answer: The सूत्रम् 2-4-77 गातिस्थाघुपाभूभ्यः सिचः परस्मैपदेषु has been used in the form अभूत् – derived from the verbal root √भू (भू सत्तायाम् १. १).

Please see the following post for the derivation of the form अभूत् –
http://avg-sanskrit.org/2012/04/16/अभूत्-3as-लुँङ्-2/

2. Which सूत्रम् prescribes the substitution ‘इरे’ in the form ईडिरे?
Answer: The सूत्रम् 3-4-81 लिटस्तझयोरेशिरेच् prescribes the substitution ‘इरे’ in the form ईडिरे – derived from the verbal root √ईड् (ईडँ स्तुतौ २. ९).

Please see the answer to question 5 in the following comment for the derivation of the form ईडिरे –
https://avg-sanskrit.org/2012/10/12/गजस्थस्य-mgs/#comment-5480