These à are not just (if at all) prepositions but infinitive markers although this concept is not yet established in French grammar.

While the most common marker is de, some verbs like se fatiguer and fabriquer might use a à when followed by an infinitive.

Je me fatigue à essayer de réparer le moteur.

but

Ça me fatigue d’ essayer de réparer le moteur.

See http://research.jyu.fi/grfle/464.html and http://gerflint.fr/Base/Paysscandinaves3/kalmbach.pdf from Jean-Michel Kalmbach for details.

In the first example, replacing à with à force de will change the meaning of the sentence.

With à, they are tired because they fight in the first place while with à force de, they are tired because they fight for a substantial period of time.

I think we could translate you sentences like that :

This is my fault, I’m sorry. We would have not get tired by fighting each
other for nothing in the village without my good idea…

the question, is to know what you’re doing by getting away like a
thief

Even if my english is a bit wrong the idea is still here and the translations are really close.
Anyway, in both case the à can be translate as by.

— edit —

The by seems a bit forced, more accurately the "-ing" verb termination seems the best suited translation.