1

There's no easy way to go back or forward in time in chunks bigger than key frames that is centered at current time/frame.

This can be done via dragging playback timeline cursor, but here comes inconvenient side effect - it's impossible to click on timeline cursor without jumping current video frame to something else. Understandably it's a feature for moving cursor somewhere else entirely, but if the click points to time within interval around current time (especially when it's a drag event start) it should assume that the click is done on exact current time and change video frame only on drag, which also should be calculated assuming that drag motion started at current time on timeline. This way you'll have a convenient way to move around current time.

Scrolling via frames (which is now on mouse wheel) is great, but this will give a stronger scroll which doesn't jump around at the beginning of the action.

2

Is it a very long video? I don't think I've had the issue you are mentioning where you click on the cursor and it jumps to a different frame.

You can also try the "time grab": ALT + mouse left drag in the video viewport. When you click down (anywhere) it will be registered to the current frame and when you drag left or right it will move relatively to that so I think it's what you are after. 

edit: actually I see what you mean on certain videos, it might be a bug in the mapping between pixels and timestamps I'll have to double check.