Mybest, I shared some of my experience which is probably about as close to yours as you'll find on this forum. In my case my husband is / was having an affair but no one should accuse your husband of the same without any certainty. My guess, based on my knowledge of how Middle Eastern men think, is that your husband is facing a combination of push / pull factors. There are things in your relationship with him that are pushing him away, that he doesn't know how to fix because he may not know how to communicate effectively, and then there are things that are pulling him away such as the idea of freedom, the ability to do whatever he wants in his own space, and possibly to date other women. He may not be actively having an affair, but he may be considering it. There are many possibilities but that would be my guess. Since you and your husband are still together, and still closely bonded, I'm not surprised that he is ambivalent about leaving. If there is any other woman out there, your husband would be torn at this time over whether she'd be worth pursuing or whether he should stay with you. Those are just guesses...it sounds like your intuition is telling you there's no affair.
If you don't wish to check secretly to see what's happening you'll be better off in the sense that you'll spare yourself the pain of knowing if your husband is up-to-no-good if he turns out to be guilty. You will preserve your love for him more easily by considering him to be loyal and faithful, which he may be. On the other hand, your husband would probably never tell you if he's having an affair. You mentioned an affair would be a deal breaker. I guess there's no deal to break if you don't know about it, so you're protecting yourself and the marriage in a way.
Deciding how much information you need about your spouse's individual actions is a personal decision for sure. Almost everyone encouraged me to check on what my husband was doing and I'm glad I did. I didn't make a habit of it, but I felt better in a way knowing it wasn't just me being a bad wife, and I felt worse in another way knowing my husband isn't the great, perfect guy I thought he was. It's very, very difficult knowing your husband is with another woman. I personally don't believe married people should have secrets, or prevent each other from accessing each other's accounts. My husband and I used to share all our passwords and everything before his affair. If you believe differently then no one can blame you for that. It just means you risk being misled, but I think over time you will start to know if your husband has a full-fledged affair. He'll likely start to ignore you much more, distance himself much more, act more wreckless, and if it's a real-life affair (not online) then he'll likely try to look better when he goes out. There are signs even when you don't investigate. If you don't see any signs, not even one, over the coming months then hopefully your husband isn't having an affair.
Hopefully your husband is just confused and frustrated and thinks the space will help. If your husband lived his whole life in the Middle East and then came here to marry you there's probably a lot of inner turmoil in his mind. His identity, way of life, and everything have changed. If you were supporting him financially there may be some resentment because that's a big shame in Middle Eastern culture for a man to live from his wife's salary.
Perhaps at the moment the best would be if your husband decides not to move out. Then you can keep working on yourself and he'll be around to witness your changes. Maybe the marriage can be fixed without a separation. That would be great!
If your husband does move out, hopefully he'll quickly see what he's missing and return. When my husband left for his first six month separation (the amount of time he requested) he was back within eight weeks.
Thankfully you and your husband are still early in the process of separating. You found this site, are practicing divorce busting techniques, and are motivated to work on yourself. If your husband is still showing affection then you two are in much better shape than many here. There is a lot you can do to improve the chances of a positive outcome. I hope this will be a temporary hurdle for you and your husband.
