Why is it needed to use here "ke"?
Is it wrong to say "Saya mau berkunjung rumah kamu"?
I want to know either. It looks like not needed.
Yes it's incorrect to omit "ke" . If you want to omit "ke" you say : saya mau mengunjungi rumah kamu.
"rumahmu" is also correct
Visit, or meet up at?
One (visit) means come over and stay there as the activity. Other (meet up) means the assembly of a group, and usually means doing something else afterwards.
"Come over sometime" versus "let's meet up for a drink sometime".
What is the difference between berkunjung and mengunjungi?