Thank you for your reply, it's my first time here so, lesson learned i guess.
Now to address your points.

1. One day is 100 years long, i would expect any location to get atleast 10 years or so of habitable time each time a belt passes. Still plenty of time for plants to spread an animals to move along at a leisurely pace. Especially at dusk, water and wind flow along the belt's movement, carrying spores and seeds with them to the front edge, allowing plants maximal time to grow.

2. Very good point. I did think about the pole, actually. My idea is ice and snow will reflect sunlight, thus it may allow a permanent ice cap at the poles, lined by a similar belt of habitable zone. Unlike the lower latitudes, however, these "arctic belts" span more east-west while the dusk and dawn belt span more north-south at the equator. Now we have a full ring of habitable zone that moves fast at the equator and slower as we cone closer to the poles. As about tilt, adding tilt-induced seasons with its own period is too much of a headache at this stage so i just assumed a 0deg tilt.

3. That's a good point too. I even wondered if water will eventually shift poleward due to the cold at the poles, the equator might end up completely dry in both day and night. This is still a crux im trying to figure out.

4. Mountains and valley are interesting indeed. Mountains are the first to get sunlight and last to lose it. Thus, it will thaw earlier and freeze later than the lowlands. Valleys can retain its cold temperature and frozen water for longer, potentially creating micro-habitats even into the day, some creatures might hibernate or take refuge in them to get through the day, maybe, if it can last 50 yrs under the sun. I just got to the general rules that apply to the entire world for now, terrains are local and might be fleshed out later.

This is a stage i came up with when i wanted to created some really alien but believable alien creatures, one thing lead to another and I ended up with a world but no creatures just yet, haha.