For the first one, you can find the tune in Lutheran Service Book, Hymn 734. That hymn, while not specifically an evening hymn, is quite appropriate for that time of day. Here is the first verse from LSB, followed by a more traditional translation from The Lutheran Hymnal (1941).
I trust, O Lord, Your holy name;
O let me not be put to shame
Nor let me be confounded.
My faith, O Lord,
Be in Your Word
Forever firmly grounded.
In Thee, Lord, have I put my trust;
Leave me not helpless in the dust,
Let me not be confounded.
Let in Thy Word
My faith, O Lord,
Be always firmly grounded.
The first hymn you hear in the evening service, though, has more nighttime themes to it.
Mit meinem Gott geh ich zur Ruh
und tu in Fried mein Augen zu,
denn Gott vom Himmelsthrone
ueber mich wacht
bei Tag und Nacht,
auf dass ich sicher wohne.
I go to rest with my God
and close my eyes in peace,
since God, from heaven's throne,
watches over me
by day and night,
that I may dwell in safety.
The second hymn you hear from this video is not familiar to me. The text and tune are neither in Lutheran Service Book nor The Lutheran Hymnal. It is considered a folk song or volkslied.
die goldnen Sternlein prangen
am Himmel hell und klar;
der Wald steht schwarz und schweiget,
und aus den Wiesen steiget
der weisse Nebel wunderbar.
The moon is rising,
the little golden stars shine
in the heavens, bright and clear;
the forest remains dark and silent,
and from the meadows rises
the wonderful white fog.
Der Mond Ist Aufgegangen with metered English Text
If you are looking for a hymn with similar themes that is more readily accessible, you can try "Now Rest Beneath Night's Shadow," (in German, Nun Ruhen Alle Wälder)which can be found in most Lutheran hymnals. The meter is the same, and the tunes are interchangeable.
In this video, you can see both German texts are used in the graphics.
Nun ruhen alle Wälder,
Vieh, Menschen, Städt und Felder,
Es schläft die ganze Welt;
Ihr aber, meine Sinnen,
Auf, auf, ihr sollt beginnen,
Was eurem Schöpfer wohlgefällt!
Now rest, all forest,
Animals, people, cities and fields,
As the whole world sleeps.
But you, my senses,
Up! Up! You should begin
whatever pleases your Creator.
Now rest beneath night's shadow
The woodland, field and meadow,
The world in slumber lies;
But now, my heart, awaken thee,
To prayer and song betake thee;
Let praise to thy Creator rise.