Here "Comme je suis [thing]" is "how [thing] I am". You can tell because of "tu as vu".
It also works with avoir :
Tu as vu comme j'ai progressé ? = Have you seen how much I've improved ?
It's hard to translate "être au courant" in a short way so it looks similar in english. I'd say it's something like :
"You see how aware I am of what's happening between you two ? I was certain you argued !"
About your last part, using "comme" alone (in the beginning of a sentence) means you're impressed by something, it's an exclamation.
Comme c'est beau ! = It's so beautiful !
A more casual say of saying is with "comment": "Comment j'ai faim !" = "Man, I'm hungry"
"Comme" can also express a cause, if it's accompanied by the consequence.
Comme vous me dites jamais rien, je sais pas si vous vous disputez ou pas.
You never tell me anything, so I don't know if you argue or not.