Hello Elida
All are fine.
"Trust me/Believe me" relate to particular acts or pieces of information, e.g.
1. "What? Cut out both his kidneys? Are you sure that will cure his myopia?" "Look, I'm a doctor. Trust me."
"Trust in me/Believe in me" relate to "me generally as a person", and mean "have faith in me", "have faith in my character/attributes/abilities".
Here's a slightly nauseating example from a Beach Boys lyric:
2. Every time we break up/You bring back your love to me/And after all I’ve done to you/
How can it be/You still believe in me?
MrP
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Edit:
Excuse the chorus. I didn't know Jim had already answered.