Learn Hardcore Russian: Хорошо бы делать короткое упражнение на дыхание каждый вечер. - It would be nice to do a short breathing exercise every evening.

Хорошо делать короткое упражнение…
= It’s good to do a short exercise… (a general statement of fact or recommendation)
Хорошо бы делать короткое упражнение…
= It would be good to do a short exercise… (a wish, an ideal, a soft suggestion)

So бы makes it sound like: “It would be good if (someone / we / you) did this.”
Without бы, it sounds more like a straightforward statement: “Doing this is good.”

Both versions are grammatically correct; the one with бы is just more like advice or a gentle “it would be nice if…”.

Where is the subject in this sentence? Who is supposed to do the exercise?

Russian often uses impersonal sentences with no explicit subject, especially with хорошо / плохо / нужно / можно + инфинитив.

Хорошо бы делать короткое упражнение…
literally: It would be good to do a short exercise…

There is no “I/you/we” in the Russian sentence. The subject is understood from context, just like in English “It would be good to do a short breathing exercise every evening” (where “it” is a dummy subject).

Depending on context, it might mean:

It would be good *for you to do…*
It would be good *for us to do…*
People / one should do…

If you really want to specify a person, Russian tends to rephrase, e.g.:

Тебе было бы хорошо делать короткое упражнение на дыхание каждый вечер.
(This is understandable but sounds a bit clumsy; more natural is:)
Тебе было бы полезно делать короткое упражнение на дыхание каждый вечер.
= It would be beneficial for you to do…

In everyday speech, the impersonal Хорошо бы делать… is very natural and doesn’t need an explicit subject.

Why is it делать, not сделать? What aspect is used and why?

Делать is imperfective; сделать is perfective.

You use делать here because we are talking about a regular, repeated habit:

Хорошо бы делать короткое упражнение… каждый вечер.
= It would be good to do (be in the habit of doing) a short exercise every evening.

Imperfective infinitive + words like каждый вечер / каждый день / всегда → regular, habitual action.

If you said:

Хорошо бы сделать короткое упражнение на дыхание.

that would normally suggest one specific time, like:
It’d be good to do one short breathing exercise (now / at some particular moment).

So:

делать → habitual / ongoing / in general
сделать → one-time, completed action

With каждый вечер, you practically must use делать.

Why is it короткое упражнение, not короткий / короткая?

The adjective must agree with the noun in gender, number, and case.

упражнение is neuter, singular.
In the accusative singular (for an inanimate noun), neuter looks the same as nominative: упражнение.
So the adjective also must be neuter, singular, accusative: короткое.

Pattern:

neuter noun: окно, упражнение, письмо
matching adjective in nominative/accusative: короткое окно, интересное упражнение, длинное письмо

So короткое упражнение is just adjective–noun agreement.

Why is упражнение in the accusative case? It looks the same as nominative—how do I know?

Grammatically, упражнение here is the direct object of the verb делать, so it is in the accusative case:

делать что? → упражнение
(to do what? → an exercise)

For neuter nouns, the nominative singular and accusative singular have the same form:

Nom. sg.: упражнение
Acc. sg.: упражнение

You recognize the case from the role in the sentence (it answers “what?” after the verb), not from the form alone.

What does на дыхание literally mean here? Why is it на, and why is дыхание in this form?

На дыхание is a very common pattern in Russian: упражнение на X = “an exercise for X / focusing on X”.

Literally:

упражнение на дыхание
= “an exercise on breathing / for breathing”

Here:

на is the preposition “on / for (aimed at)”
дыхание is a noun meaning “breathing”.
After на with this meaning (“aimed at / for training”), you use the accusative:
на что? → на дыхание

More examples of this pattern:

упражнение на память – an exercise for memory
упражнение на произношение – a pronunciation exercise
упражнение на внимание – a concentration / attention exercise

So упражнение на дыхание is an idiomatic way to say “breathing exercise”.

Could we say дыхательное упражнение instead of упражнение на дыхание? Is there any difference?

Yes, you can say both, and both are correct:

дыхательное упражнение = “breathing exercise” (adjective + noun)
упражнение на дыхание = literally “exercise on breathing / for breathing”

Nuances:

дыхательное упражнение is the more direct dictionary translation of “breathing exercise”; it sounds a bit more formal/technical.
упражнение на дыхание is very common in everyday speech and especially in contexts like yoga, meditation, singing, etc.

In many situations, they are interchangeable:

Хорошо бы делать короткое дыхательное упражнение каждый вечер.
Хорошо бы делать короткое упражнение на дыхание каждый вечер.

Both sound natural.

Why is it каждый вечер and not something like по вечерам or каждым вечером?

All three are grammatical but have slightly different meanings:

каждый вечер (accusative) – “every evening”, emphasizing each individual evening:
- Хорошо бы делать… каждый вечер.
  = It would be good to do it every evening (each day).
по вечерам (dative plural with по) – “in the evenings (as a general time)”:
- Хорошо бы делать короткое упражнение на дыхание по вечерам.
  = It would be good to do a short breathing exercise in the evenings (in general).
каждым вечером (instrumental) would mean “with each evening / by each evening”, which is not how you express habitual time in Russian, so it’s not natural here.

For regular repeated time, Russian commonly uses:

каждый вечер / каждый день / каждую неделю – every evening/day/week
or по вечерам / по утрам / по воскресеньям – in the evenings / mornings / on Sundays

In your sentence, каждый вечер is the most straightforward choice.

What is the role of каждый вечер grammatically? What case is it?

Каждый вечер is in the accusative case, and it functions as an adverbial expression of time: “every evening”.

каждый → masculine, singular, accusative
вечер → masculine, singular, accusative (for inanimate masculine, nominative = accusative)

Russian often uses the accusative to express how long / how often / when:

каждый день – every day
всё лето – all summer
целый час – for (a) whole hour

So каждый вечер answers “when?”, but it is in the accusative form.

Can the word order change? For example, can I say Каждый вечер хорошо бы делать короткое упражнение на дыхание?

Yes, Russian word order is flexible. All of these are possible, with slightly different emphasis:

Хорошо бы делать короткое упражнение на дыхание каждый вечер.
(neutral; slight focus on the action “to do a short breathing exercise every evening”)
Каждый вечер хорошо бы делать короткое упражнение на дыхание.
(slight emphasis on “every evening” – the time frame)
Хорошо бы каждый вечер делать короткое упражнение на дыхание.
(emphasizes “every evening” as part of the recommendation)

In spoken Russian, the original order is very natural, but the others are perfectly acceptable.

Could I say something like Хорошо бы каждый вечер подышать instead? How would that differ?

You can, and it’s natural, but the nuance changes a bit.

Хорошо бы делать короткое упражнение на дыхание каждый вечер.
= It would be good to do a short breathing exercise every evening.
(focus on a specific exercise or routine)
Хорошо бы каждый вечер подышать. (подышать = perfective, “to breathe for a while”)
= It would be good to take some time to breathe / do some breathing every evening.
(more general, less like a formal “exercise”, more like “to breathe deeply a bit”)

If you want to keep the idea of a structured exercise (like 4-7-8 breathing, box breathing, etc.), упражнение на дыхание or дыхательное упражнение is better.
If you just mean “it’d be good to do some breathing (not necessarily a ‘formal exercise’)”, then подышать is good.