I am the owner of Wave 3, so I think I can answer your questions:
1. Built-in Browser have average speed, comparable to Nokia Lumia 800s - there is no gpu acceleration, yet lags appear only on flash-heavy sites until they are loaded - other no-flash ones can be scrolled / zoomed even during that process without problems. Opera and UcBrowser are little bit faster, obviously lacking flash support.
2. Multitasking works well in Wave3, yet it is not a system-wide function. What I mean, that this multitasking is app-dependent and isn't so commonly implemented - for example most of the games are single-tasking apps so you can't switch between them, but you can for example switch between game and Browser/Mail/Notes flawlessly (as those app support multitasking). There are bunch of 3rd party apps that support multitasking too, as TuneIn Radio for example, but it is not yet a coding manner for bada.
3. No, you can't hide it but...
4. There is no such problems either