Hier sind die Antworten meines Korrespondenzpartners:
1) So Gott will. (God willing)
בעזרת השם.
Be'ezrát Haschém.
(this is the translation of "God willing")
2) Gelobt sei Gott. (Praise be to God. - )
השבח לאל.
Haschévach la'él.
3) Gott sei Dank. (Thank God. - תודה לאל)
תודה לאל.
Indeed, as you wrote yourself, the Hebrew would be: Toda la'él - as spelled in Hebrew on your own line.
4) Im Namen Gottes. (In the name of God.)
בשם אלוהים.
Beschém Elohím.
