Даже когда человек чувствует отчаяние, у него остаётся по крайней мере один выбор — сделать маленький шаг вперёд.

Yes. Даже means even here, and it emphasizes how extreme or unexpected the situation is.

• когда человек чувствует отчаяние – when a person feels despair
• даже когда человек чувствует отчаяние – even when a person feels despair

So the idea is: In the very difficult situation when a person feels despair, still….

Note that даже is attached to когда, not to the verb. You wouldn’t normally say когда человек даже чувствует отчаяние in this meaning.

Both are possible, but they have different nuances:

• чувствовать отчаяние = to feel despair (focus on the inner feeling, a state)
• отчаиваться (imperfective) / отчаяться (perfective) = to despair, to lose hope (focus on the process of giving up hope)

In this sentence, чувствует отчаяние paints it as an emotional state the person is in.
If you say:

• Даже когда человек отчаивается, …

it sounds a bit more like even when a person is despairing / giving up hope, focusing on the act of falling into despair. The original wording is more neutral and common in this kind of motivational statement.

Отчаяние is in the accusative case as the direct object of the verb чувствовать:

• чувствовать (что?) отчаяние – to feel (what?) despair

Neuter nouns ending in -ие (like отчаяние) have the same form in nominative and accusative:

• Nominative: отчаяние есть – there is despair
• Accusative: чувствовать отчаяние – to feel despair

No preposition is needed because чувствовать simply takes a direct object.

Russian usually expresses possession with у + Genitive + есть / остаётся / было rather than with иметь:

• у него есть выбор – he has a choice
• у него остаётся выбор – he still has / is left with a choice

Here у него остаётся literally means with him there remains.

Using иметь (он имеет выбор) is grammatically possible but sounds formal, bookish, or influenced by English. In everyday Russian, у него есть / у него остаётся is the natural way to say he has / he still has.

Остаётся is from оставаться (to remain, to be left). It suggests that:

• Something else may have been lost, but
• this still remains.

Compare:

• У него есть один выбор – He has one choice. (neutral)
• У него остаётся один выбор – He has (only) one choice left / One choice remains for him.

In the sentence, остаётся emphasizes that at least one choice remains, even in a very bad situation.

По крайней мере means at least.

In this sentence:

• у него остаётся по крайней мере один выбор
  = he has at least one choice left

It sets a lower bound: maybe he has more choices, but we’re sure he has at least one.

Position is somewhat flexible:

• У него остаётся по крайней мере один выбор. (most natural)
• По крайней мере, у него остаётся один выбор. (slight emphasis on “at least”)
• У него, по крайней мере, остаётся один выбор. (emphasizes contrast: he, at least, still has a choice)

Выбор in Russian is usually uncountable in the sense of choice as an option or freedom to choose, similar to English “freedom of choice”:

• у него есть выбор – he has a choice / he has options

You can count выборы in some contexts, but then it often becomes more abstract or means elections:

• сделать несколько выборов – to make several selections (rare, sounds technical)
• выборы – elections

In this motivational sentence, один выбор corresponds to English “one choice” or “a single choice” and feels natural and idiomatic. Plural выборы here would sound strange or misleading.

The dash introduces an explanation / specification of what that one choice is.

• …у него остаётся по крайней мере один выбор — сделать маленький шаг вперёд.

Roughly: he still has at least one choice — namely, to take a small step forward.

In Russian, a dash often connects:

• a general noun (выбор) and
• an infinitive phrase that explains what that noun actually is (сделать маленький шаг вперёд).

Сделать (perfective) focuses on a single, complete action – to make (one) step, to do it.

• сделать шаг – to take a (single) step
• делать шаги – to be making steps (repeatedly, habitually)

In this sentence, the idea is: make one small step forward (as a concrete action you can take), so perfective сделать is exactly right. Using делать would sound unnatural here.

• маленький шаг is accusative (direct object of сделать):

  • Nominative: маленький шаг
  • Accusative (masculine inanimate): маленький шаг (same form)

• вперёд is an adverb of direction: forward, ahead.

So:

• сделать маленький шаг вперёд = to take a small step forward
  literally: to make a small step (where?) forward.

There’s no preposition before вперёд because it’s not a noun phrase; it’s an adverb, like English forward in step forward.

Yes, Russian word order is flexible, and different orders slightly change the focus:

• У него остаётся по крайней мере один выбор.
  Neutral, standard: He still has at least one choice.

• У него по крайней мере остаётся один выбор.
  Emphasis that at least something remains: other things may be gone, but this remains.

• По крайней мере один выбор у него остаётся.
  Stronger emphasis on по крайней мере один выбор (at least one choice remains to him), useful in contrast with something like “others have none”.

The base meaning is the same; only what is highlighted changes.

The comma separates a subordinate clause from the main clause.

• Subordinate clause (introduced by когда):
  Даже когда человек чувствует отчаяние, …
• Main clause:
  …у него остаётся по крайней мере один выбор — сделать маленький шаг вперёд.

In Russian, a clause introduced by когда (when) is always separated from the main clause by a comma, whether it comes first or second:

• Когда он пришёл, мы начали.
• Мы начали, когда он пришёл.

Stress and rough pronunciation:

• отчаяние – despair
  Stress: отЧАяние – [at-CHA-ya-nee-ye]
  The тч is pronounced together (like “tch” in “catcher”).

• выбор – choice
  Stress: ВЫбор – [VY-bar] (with ы like a hard, back “i” sound).

• вперёд – forward
  Stress: вперЁд – [f-pye-RYOT] (the ё is always stressed and sounds like “yo”).

Correct stress is important in Russian; changing it often makes the word hard to understand or sounds wrong to native speakers.