1) Arranging flowers in the traditional manner is very difficult for me. // Flower arranging in the traditional style is very difficult for me. // I find traditional flower arrangements to be a very difficult task for me to do.
(all of it sounds a bit awkward. Why not just say, I'm terrible at making traditional flower arrangements // I'm terrible at traditional flower arranging. ?)
#2 is fine
3) We typically say: Arguing doesn't solve anything. Or you could say: This argument won't solve any problems.
In answer to your additional question, it depends on whether there is both a noun form and a verb form of what you're trying to say. In normal life, most of us don't arrange flowers (or even talk about it) therefore that's sort of an odd verb choice + noun for us.
Also, when choosing whether to use active verb (ing) or supplementary verb + noun really depends on what you're trying to say, ie what is the key point of the sentence. Do you want to tell us that you're actively doing something or do you want to focus on the object?
Besides just constant immersion in the language, the only way you can really understand the best use is by increasing the amount of reading and listening you do of English. Over time you will develop a better ear for whether to use active tense verbs or verbal phrases. According to my high school English teacher, the best words to use are active verbs and very descriptive adjectives.