Does it sound ''english''?

These are all sentence fragments. Are you using them for advertising? Because otherwise, by definition, they have problems. You need verbs in sentences; these just look like clauses and they have no context to them.

But let's assume you meant to use fragments.

1) Use 'with'. It's not a great statement, and prodigious is just not a word you hear that often these days. Extensive is probably closer to what you want to write.
2) This one is, as you correctly pointed out, nearly identical to the first. At least you have a verb (giving) but you don't have a subject. Who is giving people the benefit? You? Me? Jennifer Lawrence? A lot of languages seem to allow the subject to be absent, but English really isn't like that, at least not without context. Furthermore, the verb is incomplete. When you use the gerund form (giving, loving, sending, etc.), you need to pair it with a form of the verb 'to be'. Therefore you should write something more like They are giving people the benefit of their extensive knowledge. Or, more simply stated: They give people the benefit of their extensive knowledge.

Between the two of them, #2 is just a shade better, but neither of them are complete sentences.

3) Are you suggesting that someone is beating someone else up in the name of love? Are you suggesting someone is an abuser? Because that is what that sentence means. Do you mean clumsily? Unconventionally? This sentence has an extremely negative connotation and it, too, does not work idiomatically in English, and it is not a complete sentence, either.
4) This is still a fragment. And the irony is utterly lost because there is no subject to it and no context. Who is leaving this legacy? The Pope? Justin Trudeau? Your teacher? Changing the adjective is not going to help this one. You still need a subject, and you still need a form of 'to be' in order to complete the gerund form.

I know English is not an easy language to learn. All is not lost! These are small fixes for the most part. More importantly, recognizing where the issue is - that is very important. If there is a problem with a verb, then changing the adjective will not fix it.

Kiki if you got my other'n you can see how much more advanced Jes than I. But my inability bein' the reason unable to post it, due to a persistent software glitch, Jes, which I'm sure you'll eventually look inta wontcha

Kiki I hafta explain Jes is an a2k Mgr, a most helpful contributor incidentally

What a great and very meaningful answer! Much more than I could have ever imagined! Thank you a lot!

I apologize for the lacks concerning the context (I thought that a very developped subject would get less interest or answers )

But it is important to summaze it a little in order to make my aim more understandable: in fact, the sentences I am presently working on will be showed in a short film (as intertitles). More precisely, each one of them will preceed a filmic sequence - and I need them to be short and simple as the pictures will be more important and illustrative.

If you want, every fragment is a part of the same sentence. I didn't mention the very first one - the beggining - which is: Then... They arrived...

So the order is:

0) Then... They arrived...

ILLUSTRATION / IMAGE (fanatic soldiers arrived)

1) Giving people the benefit of....

ILLUSTRATION / IMAGE (fanatic soldiers killing believers)

2) Spreading love...

ILLUSTRATION / IMAGE (still killing etc.)

3) etc.

It is always the same subject (they, the fanatic soldiers), and I didn't want to repeat it in every intertitle. Am I clear? Do you understand what I want to do?

For the 3) : Spreading love a little roughly. You have the correct interpretation: indeed, this sentence is meant to be ironic. In fact, the text will be followed by a massacre (showing fanatic soldiers killing believers). So of course, it is not real love. In this context - and even if it must be difficult for you to apprehend it - do you think it can work? Or is the ''a little roughly" not english sounding at all?

What do you think of : ''Spreading love clumsily''? Better? At least, is the idea and formulation of ''spreading love'' correct?

4) Leaving an invaluable legacy: this text is supposed to be followed by ruins. Again, it is totally ironic (in the filmic sequence, fanatic soldiers have killed everybody, and there is nothing remaining, only rubble).

I have a last question, if you can help me: what do you think of ''working valiantly for a better world''? (I mean that people want to make the world a better place).

Oh, thanks.

And now I get what you're trying to do. Basically, the intertitles work as one long sentence throughout the film.

I would say, for this particular usage, you're fine without the subject. It's understood from both the beginning of the sentence/film, and it is also understood from the visual cues you're giving with the video portion.

Given that context, I would definitely go with 'a little roughly' as it makes it a lot clearer to the viewer that it's not clumsiness or inattention or the like - the soldiers are raping completely voluntarily.

I think the last bit (do you mean that to be the title for the entire piece?) - that could be good.

Maybe even go shorter, something like Making the World a Better Place. That would be idiomatic in English and it would take 'valiantly' out of the equation. Then the viewer really would be shocked at the action on the screen.

I hope this helps - it sounds like a really interesting project. Best of luck with it.

Thank you jespah for your great and clear english!

I feel so much better now you are able to understand it

I am particularly happy that you agreed with the ''a little roughly'': I will keep it. Great

""Making the World a Better Place. the viewer really would be shocked at the action on the screen"" : you have perfectly understood the whole thing! Great again

This sentence will be followed by apocalypse - the paroxysm of fanaticism: fire and bombs exploding everywhere etc. (the screen will be totally under fire, dust, explosions etc.). So the text ''Making the world a better place'' will be perfectly fine and ironic

Again, thank you very much for helping me.