1. Bruce is trained in multiple martial arts and has extensive experience fighting metahumans, and is in peak human condition-- but lacks superpowers in that department, so I'm hesitant to say he could definitely beat her or she could definitely beat him. I guess I'd say a good measure might be how you think a fight between Monet and Steve Rogers might go?
2. Yes... sort of? Bruce has been shown in canon to have some tricks to circumnavigate mind-reading, but they're not absolute. She'd have to work for it, but that in and of itself would probably give something away about Bruce Wayne.
3. I'd say they're at about the same level, so... probably, but it would take significant time and effort.
4. Probably about the same?