1)
Is this connected to the previous verse?
1.
Malbim: Yes. They say that Hashem wants to kill me. I am confident, for I know that He will help me (refer to 56:5:2:1).
2)
Why does it say "Elecha Evtach"?
1.
Radak: This is like Alecha (I rely on You). Also "Betach El Hashem b'Chol Libecha" (Mishlei 3:5, is like Al Hashem).