Let's start with removing idioms and colloquialism
In a relationship, you need somebody who will complain when you've done something wrong, and not someone who ignores (forgives) your faults.
First, "gonna" is a colloquialism for "going to". The standard future form "somebody who is going to..."
"Call you out" is an idiom meaning in this context telling - sometimes even in a harsh way - that you did something wrong; reacting to your doing.
"let something slide" is an idiom that means overlooking/ignoring some fault on purpose. Say, you were going 80mph on a road with speed limit of 60mph. There was a policeman with a radar, and they did notice you speeding. They did not stop you, no ticket, no fine, nothing - they let it slide. It's not the same as not seeing the fault - it's choosing not to do anything about it.
Your original sentence means that for a successful relationship you need a honest feedback from your partner. If something you do ires them, they should tell you. If you keep doing something wrong and they never protest, it damages the relationship.
If we look up the preposition "with" in a dictionary, we'll find that the "with" is used in different senses apart from its main use to say that two or more people or things are together. For example, it also means because of or in reaction to, regarding, using or by means of, having, etc. So when we say that the kids were screaming with excitement, it means that that they were making a loud and high cry because they were excited. One screams with a strong emotion such as anger, fear, pain or excitement. As for sth, it is the abbreviated use of something.
Best Answer
I would presume it means to submit your homework to your teacher.
But as StoneyB says, we normally say "turn in" or "hand in".
In general, to "give in" means to surrender, to let someone else have their way. Like, "Al wanted to go the car show but his girlfriend Mary wanted to go to the ballet. Finally Al gave in and they went to the ballet."