Ratios only matter in vibrations (frequencies) because the vibration is a non-uniformity within a period. Translational speed isn't like that.
The main point of special relativity (Lorenz transform) is that it is a mapping between [0, c] and [0, infinity], so ratios to speed of light are not absolutely definable. Light has infinite speed in its own reference frame.
Not really AFAIK, since it's an asymptote regarding your speed vs speed of light, so it's a pretty continuous curve. The point where things become weird is at close to the speed of light so in your example at like 1.9~1.999 m/s, and physics "break" at 2m/s, but there's not a sigle point between 0~1.999 where anything "surprising" happens.
I feel like your field of vision expanding and everything around you freezing might be considered surprising. These don't become noticeable until near the top end.
Things get "weird" non uniformly at all the various fuzzy intervals where the effects of relativity are significant in scale compared to the measurement error, in time and space dimension, of whatever phenomena you are studying or experiencing. There are many of these phenomena at different scales, and which ones you care about is subjective.
I imagine there has to be some special properties when youre at exactly half, or some other special ratio of the speed of light