How can I trigger protecting Zach from demotion?
You have to be on the sub route to do this. While on the loser track (k4), just before you and the boys (Jake, Zach, Kane) are awoken in a dumpster by Scarlett and Delilah you'll need to select the third option 'I need to focus on Zach. Jake is streetsmart and tough. But Zach needs to be motivated with some kind of positivity to help him. I'll try that.' which will give the variable zachopts +=1 which will later keep him at k4.
How can I get better rapport with Kwame? It seems that I simply don't get choices for those outcomes and I can't understand why. Do I need to start as K4 or K5 for that? Do I need Dominique as a sponsor? I usualy play the dom route with Victoria as a sponsor and start at the K6 rank.
Starting at k5 is generally how to increase your rapport with him since you two will be in the same cell and you'll have lots of dialogue options with him.
But if you're on the dom route and managing your female pod, after the scene where they have to smash crystals Dominique will visit you and she will ask you about Kwame. (this is regardless of whether you started k5 or k6 and regardless if you have her as a sponsor or not)
If you passed her secret test, she will ask you to befriend him and betray him.
If you didn't pass her secret test, then she will ask if you're willing to stick your neck out for him or not. If you say you are, you'll gain points with him. If not, you'll lose points with him
Do I need Dominique as a sponsor?
Err, for what?