If the speedrun is in 480p quality, will it be counted or is it necessary to have hd?

As long as the moderators can tell what's going on, then it'll probably be fine.

It depends on the game... If the category rules state that certain things must be visable, then a low quality video might not be accepted. Also pay attention to rules to fps -> e.g. if a game runs on 60fps it could be that the moderators want to verify this in your video, so it should be recorded on 60fps too.