This will depend on what type of divorce was conducted. If it is raj'i (revocable), and within her 'iddah period, then they are husband and wife again.
You have no obligation according to Fiqh standards. The matter of honesty and friendliness and... with your spouse is something else. You have to manage it according to her types of manners and how demanding she would be in future.
Yes, you can do that, as long as she is ok with you being away from her, and try your best to either bring her to where you live, or finish your trip and return back to live together.
Husband and wife in general should be living together regularly.
As for seeing each other, etc, that is also permissible, but you correctly said "without masturbation".
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