If a man living in Israel would learn less torah than if he lived in Chutz La’aretz would he be permitted to live in Eretz Yisrael? a] Would he be permitted to reside permanently in Chutz la’arez? b] What are rav Kook’s views on the matter?

I have discussed this matter in the past with Rav David Samson, a close student of Rav Kook (the son) and a world wide known authority on Rav Kooks' (the father) writings. He quoted several Gedolim including the Chafetz Chaim that held very clearly that one can not make Hashems' "book keeping". We are servents and as such we do what we wre told, the Torah includes a Mitzvah to live in Israel and you have no right to avoid fulfilling this Mitzvah for imaginary personal excuses. You do your part of the deal – the Mitzvah to study and Hashem will take care if his part of the deal and allow you to grow in Torah. Similarly you have no guarantee you will study Torah outside of Israel and not in Israel, the title Eretz Ysrael vs. Torah is deceitful. It is true that if you have a specific rabbi or Yeshiva you really want to study from and can't find your place in the Yeshivot in Eretz Yisrael – you have permission to leave, as the Rambam (Melachim 5:9) states, however then also only temporarily.