This is an incomplete answer. I think the word may be:
My first could describe a call or a fell, in two ways,
And it sounds like a way of going fast in olden times.
High - You can describe a phone call as just saying hi (high). You can describe someone's fall or a tree fell as being high. As @humn stated, Hie could be a term for going fast in olden times.
OP edit: the adjective "high" can mean high-pitched (as a call/shout can be) or high altitude (as a fell/mountain can be).
My second could describe a paper or a cloud, in two ways,
And docked it's almost my first, but not in truth.
Light You can describe paper and cloud as being light (lightweight). A cloud is visible because of sunlight scattering particles through tiny droplets the atmosphere.
OP edit: the adjective "light" can mean light-coloured (like white paper and white clouds) or lightweight (again like paper and clouds which don't weigh much).
My whole is used to know what's important,
Like for instance a featured SE post.
Highlight means to emphasize or make prominent. You could say that a featured post is highlighted to get more views.
At time of posting, the current featured post is amusingly: