Translations/quotations in normal type, and my own comments/interpretations in the italics. I am quoting the parts where the sandhi may be a bit tricky - by undoing the sandhi. Not quoting the other parts.
'ननाद' इति अत्र अन्तः-भावित-णि-अर्थः। 'नादयामास' इति अर्थः। = ननाद here has an implied causative (णि/णिच्) meaning, i.e. the meaning is नादयामास। (Basically, ननाद is normally supposed to be intransitive, but here used as transitive/causative.)
विमर्शे - the sense is "I deliberate and clarify", i.e. "I make a clear deliberation".
Since मृशति is परस्मैपदी, (here we have) exceptionally (=व्यत्ययेन) the first person singular of आत्मनेपद, where because इट् becomes/behaves like ङित्*, गुण does not obtain (गुण-अप्राप्तौ अपि < अप्राप्ति), yet exceptionally (we have) गुण|
*"इटो ङित्" seems to refer to some rule of grammar, but I don't really speak पाणिनि - so not sure exactly what the rule in question is. In any case, the idea is that in this interpretation, the expected form is परस्मैपद "विमृशामि". Even if we allow आत्मनेपद as an exception, it should have been विमृशे without गुण. The actual form विमर्शे requires an additional exceptional गुण on top of the आत्मनेपद usage.
अथवा सप्तमी-अन्तम् एतत् पदम् = Alternatively, it may be a form in the locative case.
विमर्शे = विचारे कृते सति प्रति-इमः इति शेषः
This one is difficult to translate directly because of the idiom इति शेषः (=to be supplied, implying an ellipsis) and the use of the locative absolute (भावे सप्तमी). So just paraphrasing: "विमर्श means विचार (deliberation); and after that we have to supply 'having being done, we believe'". In other words, विमर्शे stands for "we believe after having deliberated" by an ellipsis.
It is to be kept in mind (=धातव्यम्) that many later authors use ungrammatical forms in their works in order to pass them off as आर्ष (i.e. composed by the ancient ऋषि-s)।
इह अपि एषा युक्तिः आस्थिता इति प्रतीयते = This argument seems to apply also here.
In summary, the commentator rates this verse as having a late origin and containing bad grammar.
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अन्तर्भावितण्यर्थः = (having) an implied causative meaning
परस्मैपदित्वात् = because of its परस्मैपदी-ness
व्यत्ययेन = exceptionally, as an exception
प्रतीमः = we believe (present 1st plural of प्रति-इ)