Learn Russian: Солнце начинает всходить, когда мы ещё спим. - The sun begins to rise when we are still sleeping.

The prefix for upward motion is originally вз-. However, Russian spelling rules require the з to change to с when it comes right before a voiceless consonant. Since the х in -ходить is voiceless, the prefix becomes вс-. You will see вз- before vowels and voiced consonants, like in взлетать (to fly up).

Why do we use the imperfective verb всходить after начинает, rather than the perfective взойти?

In Russian, 'phase verbs' that describe the beginning, continuing, or ending of an action (like начинать, продолжать, заканчивать) must always be followed by an imperfective infinitive. The grammar rule of 'begin + imperfective' takes priority here.

Since the sun is making a single trip upwards, why does всходить use the multidirectional root -ходить instead of the unidirectional -идти?

When you add a prefix to a verb of motion, the core rules change. Adding a prefix to a unidirectional verb (like идти to make взойти) creates a perfective verb. Adding a prefix to a multidirectional verb (like ходить to make всходить) creates its imperfective partner. Because we need an imperfective verb after начинает, we must use the -ходить version.

I usually translate ещё as 'more'. How do we know it means 'still' here?