Hi,
First the speed sliders. They are locked together until you change the settings in Preferences > Playback > General > Link speed sliders.
In general you shouldn't have to change this option. The preferred way is to adjust the high speed video settings (Motion > High speed camera) of the slow motion GIF.
In your case it's a bit special because the animated GIF was probably not shot with a high speed camera but rather slowed down programmatically at creation.
You can still fiddle with the high speed camera settings until the info in the bottom part of the dialog "Video is x times slower than original" matches the slow motion factor of the GIF, if you know it.
All this is not strictly necessary, but it's the more correct approach I think. It will display proper times and let you use stopwatches on the slowed down GIF for example. And the normal speed video will be automatically slowed down to match the GIF speed. And you will be able to use the speed sliders.
About the common frame navigator.
There are two different mechanisms, the common play button works by calling play and pause on the individual videos at the right time, to honor synchronization (based on speed settings of each video).
However, the common frame navigator, next button, previous button, etc. and the saving process, all work at the frame level, which causes the problem I think you're having.
Although I used to consider this an unfortunate limitation, I now think it's a bug induced by not using the right approach.
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Thought a bit about it last night. The following might not make sense without the code, I'm writing it down to remember it 
I think it is possible to express synchronization in terms of scaling and translating of two 1-D variables (the videos).
The scaling will map the fps from one video to the other (taking any slo-mo in account), and the translating will express the shift due to the synchronization point.
With this I think we can start with any time coordinate in the first video and find the corresponding time coordinate in the second video.
b = (a-t) * s.
b: time in second video.
a: time in first video.
t: translation = position of sync point in first video.
s: scaling = (fps of second video / fps of first video). (actual playing fps, not necessarily original fps of video).
Hopefully this will someday allow proper frame level synchronization.
