First, let me transfer to permanent storage some points I made in comments.
Spanish as you have observed uses the gerund a great deal: sometimes with auxiliaries, sometimes with verbs of motion, and sometimes with any verb whatsoever. In English, we using ‑ing words a lot, too, but not always in the same way.
I feel that using a Spanish gerund with an auxiliary verb is not so different from using it with any other verb, such as a verb of motion like andar, llegar, venir, salir “walk/go around, arrive, come, go out”. These verbs of motion better lend themselves to a near-identical treatment in English: Vino corriendo a verme “She came running to see me”, but verbs that are neither auxiliaries nor motion verbs do not so easily taking -ing verbs in English without some preposition or conjunction to connect them in an adverbial circumlocution.
The frequent need for a preposition or conjunction in English also derives from how in Spanish, a gerund is always an adverb, whereas in English, a gerund is by (rather useless) definition a noun, and when the ‑ing word is acting as a modifier be it adverbial or adjectival, (some) people tend to call it a participle instead.
Sometimes these are differences without distinction, and there are many circumstances when it is best simply to call it an ‑ing word and forget about gerunds vs participles.
Nonetheless, the “modifies a verb” aspect you seek is still more readily done in English with extra joining words, namely prepositions or conjunctions, then my direct attachment to verbs that are neither auxiliaries nor verbs of motion.
As I elsewhere wrote, these nuances can be tricky to convey in English; a word-for-word translation is almost always going to be too clumsy for practical use.
Sometimes adding an adverb is enough; other times a different verb is needed, or a different sort of periphrastic verb. The loose translations below are all meant to be idiomatic in casual, spoken English. In some cases I give more than one possibility because no one of them quite hits the nail the head.
For simplicity and consistency, I’ll use he for the implied third-person pronoun of Spanish, although of course she or you (formal), and sometimes even it, are all equally applicable, since in the general case and without further context, we cannot know whether the implied antecedent is él, ella, ello, or Usted.
Elements in square brackets are implied, but probably wouldn’t be included in most translations.
Está buscando piso.
He’s looking for an apartment.
(idea of unfolding action in general)
Anda buscando piso.
He’s out looking for an apartment.
He’s still looking for an apartment.
He keeps looking for an apartment. (although sigue is better for keeps)
(idea of repeated action)
Los precios van cayendo.
Prices are falling.
Prices have begun falling.
Prices have started to fall.
(idea of progressive action
starting in the present)
Los precios vienen cayendo.
Prices have been falling.
(idea of progressive action that started in the past)
Sigue comiendo a las dos.
He’s still eating [lunch] at 2 o’clock.
(idea of persistent action)
Lleva dos años saliendo con Marta.
He’s been going out with Marta for two years.
(prolonged duration of an action that began in the past)
Salió corriendo del colegio.
He took off running from [the [high]] school.
All of a sudden, he left [the [high]] school at a run.
(action that starts suddenly and then continues)
Progressiveness doesn’t always map between languages. For example, sometimes the sense of “ir a + infinitive” may be better translated into a progressive construct in English, even though it wasn’t one in Spanish.
For example and in particular, the initial “que voy a mencionar” from the previous question on the other SE site seems a better fit for “that I’ll be mentioning” instead of the more direct translation of “that I’m going to mention”. This demonstrates how the progressiveness aspect does not necessarily map one-to-one between the two languages.
For your specific examples, I might suggest these. Sometimes it’s best to treat the -ing verb as a noun in English and then use a preposition to connect it adverbially to the verb. In other cases, an actual subordinate clause might work better. Whether you wish to retain the progressive aspect is sometimes more of a matter of choice than a mandatory element.
Here are several takes on your own examples:
El alma es dichosa dando y sirviendo.
The soul is blessed by giving and serving.
Blessèd is the soul that gives and serves.
El niño anda bailando.
The boy is out dancing.
The boys goes around dancing.
El artista vive provocando emociones.
The artist makes a living by provoking emotions.
The artist lives through the provocation of emotions.
¿Porqué hablas gritando?
Why are you screaming?
Why are you shouting when you talk?
Why do you shout when you speak?
Why do you talk by shouting?
There is no one right answer here. You need to know what seems idiomatic in the target language, which might require the addition of some other words that aren’t strictly verbs themselves.