Assalamu alaikum,

My YouTube channel is called Rashidun Caliphate and I have subbed to Blessed is HaShem the God of Israel, and I saw him saying "Shalom Aleikhum" which in Arabic is Assalamu alaikum, and I responded with waalaikum assalam in Arabic and not in Hebrew. Because, my intention is to prove tolerance and respect.

My questions are:

1. Have I committed disbelief?
2. Was it ok what I did since I had good intentions?
3. Is it ok if I want to greet my cousins who are Jews with Assalamu alaikum since I'm Arab and I come from Ishmael and Jews from Isaac?

Jazakhalakhair