नमस्ते श्रीमन् रायवरपु-पवनकुमार-महोदय !
In देव +आलय; - देवालय; the Sandhi is done, because it is compulsory to do Sandhi, when composing a compound word.
However नायक is not a compound word. It is a derived word. In Sanskrit, words are "derived" by affixing prefixes प्रादयः (उपसर्गाः क्रियायोगे) and suffixes प्रत्यय-s. Understanding "derivation" of a word is understanding its etymology. The word नायक is derived from धातुः नी.
Etymology or derivation is not simple. To put etymology of नायक from नी, may I put it as नी => नय् => नायक. As can be seen, न in नय् has become ना. That is a वृद्धि-प्रक्रिया
ना is not to वृद्धि-प्रक्रिया. But by वृद्धि नी becomes नै only and before अक it becomes नाय्+अक = नायक by आय् आदेशआ, and then declined as नायकः!
and not a संधि of ने+अक.
Actually संधि of ने+अक would become ने$क, not even नयक. because in the instance of एङ: पदान्तादति the सूत्रम् एचोऽयवायावः does not apply.
Wrong. ने+अक ए is not in पदान्त and does not take पररूप. It will become नयक only. Here the splitting is incorrect.
The root cause of your confusion is due to your premise that नायक is ने+अक. It is not.
नी is the root meaning to carry/lead and ण्वुल् is the suffix becoming अक having the meaning doer. Both give give the meaning one who leads, i.e. leader.
अयादिसन्धि means ए, ओ, ऐ, औ takes अय्, अव्, आय्, आव् respectively before vowels.