Can a character dodge/fly if they use up all their speed?


There’s something about the language in the rules for Dodging and Flying that confuses me. In both cases, both can only performed so long as the character’s Speed is not ‘reduced to 0’.

By that logic, if a character with 30 feet speed, were to say use the full 30 feet speed on their turn, would that prevent them from taking the Dodge action?

Likewise, if a creature had, say, a Flying speed of 60 feet, would there character have to fly 55 ft in order to stay aloft or risk falling?

(As a side note, how do attacks like Thunderwave which force movement play into this? If a Thunderwave hits a 30 feet speed character who has only moved 25 feet, would that prevent the character from being able to use Dodge until their next turn?)