Thank you so much for introducing me to this singer. It is beautiful.
The name of the first song is: ויהיו רחמיך מתגוללים על עם קדשיך
May your mercies be scattered over your holy nation
In the second song it starts out:
Hashem is the king, Hashem ruled, Hashem will rule for ever and ever
Melech is king
It's a bit hard for me to undertand his accent, it's not a modern Hebrew accent, but yeshivish accent.