Ok, so after investigating, it was always intended that her move speed is increased, so the description is wrong. It will be fixed in the next patch.
After discussing with the lead dev about the cast time, the explanation is fairly simple. The 3s represent the duration of the cast "charging" animation, and the extra time you're experiencing is the cast "launch" animation, that is not reflected in the tooltip.
In general, the cast "launch" animation last around 1 sec, and the spell goes off in the middle. It is more visible with Nella as her casting animation are more spectacular and the spell effect tends to take a bit more time to happen.
As for Motcha, the number is wrong, it is 800% (tooltip will be corrected in the next patch). His basic regen is 7 and the duration being only 5sec, it's not overpowered. But it makes mana regen stacking really interesting
