Are Gotic "h", "k" and Russian "с", "з" cognate only before and after Gothic "ai"

Are Gotic "h", "k" and Russian "с", "з" cognate only

before Gothic diphthong "ai"

haírto сердце
háims семья

and

after Gothic diphthong "ai"

taíhun *desętь десять
saíhs *šestь шесть
taíhswa *desnъ десница

and

before Proto-Germanic *ū

*hurną *sьrna серна
*kurnô *zьrno зерно
*hundą *sъto сто

Have normalised transliteration of Gothic diphthongs based on /h/, /hʷ/, /r/ and centum - satem got a relation ?

I mean

Is accented centum diphthong aí + /h/, /hʷ/ equal to satem "s"?
Are /h/, /hʷ/ + accented centum diphthong ái equal to satem "s"?