Gah, I had written a longer reply, but accidentally updated the site so I guess it disappeared in cyber space. Your input was much appreciated anyway and I learned/relearned a lot! And felt slighty embarrassed for some obvious misses! 
The answer key says:
Pyrrhus, rex Graecus, pecuniam dedit Fabricio, duci Romano, ut exercitus Romanum proderet. Nullum autem donum tantum erat ut Fabricium temptaret. Graecus quidam ad castra Romana venit ut donum acciperet et tunc regem interficeret. Sed tam probus erat Fabricius ut hominem regi redderet ut ab eo puniretur.
I don’t really think the last sentence looks that neat though… If we’re not going to use pronouns, isn’t it much better to just write …Graecum redderet… rather than hominem? Seems really weird to me at least. And, as has been pointed out before, the double ut-clauses doesn’t look good at all.
Here comes exercise 21 and 22 and my questions. I have double and tripled checked everything, so I don’t think I can do much better than this. Very tired today as well… 
Exercise 20:
1. Sperare facilius quam credere est.
2. Qui imperare volunt, parere discere debent.
3. Dux bonus (esse) putabatur.
4. Pro patria moriri volere est officium militum omnium.
5. Desine ignavum esse, et laborare doce!
6. Amicis subvenire constituerimus.
7. Hi pugnare non solent.
8. Amici veri tibi visi sunt?
9. Dux castra in colle ponere constitit.
10. Mentiri non ausi sunt.
11. Nonne domum relinquere cognatus es?
12. Nos in urbe remanere non sinunt.
Exercise 21:
1. Iuvare pauperes conari est (res?) civium bonorum.
2. Discere facilius quam docere est.
3. Si milites contendere nolunt, puniuntur.
4. Ipse sibi prodesse cupit.
5. Barbari fortes (esse) dicuntur.
6. Se hostem in urbem sequi constituerunt.
7. Iuvare eos, qui ipsi suos iuvare possunt, iucundum est.
8. Omnes mentiri turpe esse putare debent.
9. Alii imperare, alii parere solent.
10. Qui alios imperare solent, parere discere debent.
11. Moriri pro patria stultum (esse) putant.
12. Omnes laudare eos, qui sapientes (esse) videntur, debent.
Question 1: I have read that Romans didn’t really like to put a lot of infinitives or words on -orum/-arum and the like next to each other. So, I wonder if you think it would be better to perhaps use a gerundivum in sentences 20.2 and 21.10?
**Question 2:**In I’m not really sure how I shall express “It is (the part) of good citizens to try to help the poor.” What confuses me is how to translate “It is the part”. Would it be fine to go with res, or can you skip it and just have civium bonorum as a genitivus proprietatis (don’t know the English term, sorry!).
Question 3: In 21.8 there are a LOT of infinitives… Do you have any suggestions for a neater solution, or is mine fine?
Question 4: 21.12 could potentially be misunderstood. It’s supposed to mean “All men ought to praise those who seem to be wise.” But it could be interpreted as “They ought to praise all those who seem wise.” Should I worry about that, or do you have any suggestions as to how we should translate it in the cleanest way possible? Is perhaps something like Qui sapientes (esse videntur) omnibus laudandi. a better way to say it?
Thanks in advance, again! Really appreciate the feedback you have given me!
A few pages of Cicero, and then it’s bedtime for me! Bonam noctem!