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To answer the main question, no—the owner goes into the genitive case, not the thing being owned. It's like the 's in English: you say Quintus's studies, with "Quintus" getting the special marker. So if you wanted to be very explicit about whose studies they are, you could say studia Quintī. You could also use the possessive adjective suus -a -um &...
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omnium elegantissima: The form of omnium is genitive plural, dependent on the superlative: 'most elegant of all.'
acuat…exerceat…oblectet…doceat: Note that these 4 verbs are subjunctive. The construction could be the so-called relative clause of characteristic, which is generalizing and can be used to talk about the characteristics of a broad class: 'that ...
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Leaving est implicit is common, especially in succinct sayings like this.
Punctuation works differently in different languages and classical Latin had almost none.
It is good to remember that all punctuation and capitalization in classical texts are due to much later editors, not the original authors.
Supplying a comma makes sense here.
To me the most ...
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A. The translation of ex aequo demulcens will have to takes its cue from mentem acuat, and to a lesser extent 'exercises...' 'delights...' 'teaches...' Perhaps translate as
'stimulates the mind...- equally soothing' (the soul, eyes, ears)
or as
'excites the mind...- equally calming'
B. concentu carminum etc for a modern audience draws attention to all ...
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