Hello Dilly. Just back from my hols and catching up with everyone's situation. You sound like you're doing well. It is interesting you feel better when you have less contact with H and that he's so nosy about your life while being so deceptive with you. He is entitled to privacy, but the lies about his phone are just that - lies - and that matters.
There's a couple of things I learned about how to deal with unwanted questions when I worked in an environment where I had to keep the attention focused on the client and not reveal anything at all about myself. The first thing is to reply to a question very briskly, then ask a follow up one of your own.
H: where are you going? Dilly: Just out to a bar with some friends. How about you? Do you have any plans for tonight?
This is the light, friendly, first-resort conversational version.
If he persists after that, you can draw his attention to it in a non-blaming kind of way.
H: where are you going? Dilly: Just out to a bar with some friends. How about you? Do you have any plans for tonight? H: which friends? Dilly: Why do you ask?
The 'why do you ask' is quite a powerful question because it puts the focus back on the person asking the questions. You don't open up an argument - you're not saying, 'we're separated, this is none of your business' or 'you're getting nothing out of me until you stop lying to me about your phone' - instead, you're just refusing to let the focus be on you having to service his need for intimacy by asking questions, and instead putting the focus on his need to pry and probe. (Hope that makes sense).
I used both these techniques in my work. I had great results with the first one - you have to be on your toes and good humoured about it but it does work. The second one tended to provoke 'just making polite conversation' or a defensive response. If you get the 'just making polite conversation' you can just follow up with a question of your own.
'I see. Tell me about you. What are you doing tonight?'
after all, if the person only wants polite conversation, they'll have no objection to you making it in the same way as they do - by asking questions about their plans.
Hope this is useful. Keep going. I sense you taking your power back and he won't like it - there will be some kind of tantrum from him eventually - but that doesn't matter - whenever the future of your R you are entitled to have some equality and dignity. He's lying to you. Don't forget that.