All of these words are used by hikers in the US, along with others.
As is usually the case in English, the Latin-derived words (ascend, ascent, descend, descent) are more formal. They’re perfectly correct but I’d be less likely to use them in speech.
‘Slope’ often refers to a geographic area, but if you are talking about the trail itself, it’s used with an adjective.
We saw a bear on the opposite slope.
There’s a steep slope coming out of the canyon, but the rest of the trail is fairly level.
‘Uphill’ and ‘downhill’ can be nouns, adjectives, or adverbs.
There’s too much uphill on this hike! I’m tired.
The last place to refill your water is on the downhill section of the approach. The climb to the summit is bone dry.
I like doing this loop clockwise. You walk uphill for 3k while you’re fresh and then finish with 7k of gradual downhill. (In the US we use ‘miles’ not ‘k’ though)
My typical day crossing the Alps was 30k with 1500m vertical. (=ascent)