Why are Proto-Germanic *fraiwą and Old Norse frjó / fræ (oblique stems frjóvi / frævi) cognate? I don't understand why are PGmc ai and Old Norse jó / æ cognate?
The part of the table "History of Old Norse and Old Icelandic vowels" from here
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The development of Proto-Germanic ai in the North Germanic languages is very complex. It depends on a number of factors (stressed/unstressed, followed by w, r/R, h etc.) - see e.g. Sandøy 2017
PGmc. ai > Proto-Norse æi (Fulk 2018: 70), which further developed into:
In your post, you ask about frǽ (and its variant frjó; Zoega 1926 says that fræ was "sometimes in old MSS. spelt freo or frjó (q.v.), but less rightly").
As you can easily notice, we have w after the diphthong in PGmc, which means PGmc ai developed into æ in Old Norse (see above), cf. Fulk 2018: 70
"In addition, Proto-Norse æi developed to ON æ (i.e., /æː/) before w (which might be lost, §6.14), as in *aiwīn- > OIcel. ævi ‘age’ (cf. Go. aíws < *aiwaz) and hræ ‘corpse’ (cf. Go. hraíw)."
Note: the acute and the macron are used interchangeably here, to indicate length.