I'd like to know a strategy to deal with this lexical issue of the Arabic language. What strategy should I follow to memorize the right pattern correctly?
As included in their definition, "broken plurals" in arabic are irregular. As a consequence, no single rule can allow you to master them. What's more, they sometimes differ so much from the singular that the word is difficult to recognize if you only know its singular form.
As frustrating as it may seem, I think the only way to memorize these plurals is to hear them several, respectively many times. The strategy I would recommend is to consistently look up the plural of new words you learn, and ask yourself what the plural of words you already know is. It reminds me of German, where I think it is important to always learn the gender of nouns. Once you get used to this discipline, you knowledge of plurals should improve a lot.
you can use these rules to get the verbal nouns, they tell you how to get it depending on the number of letters in your verb and the vowels on some of those letters.
I wouldn't bother to learn the rules by heart. If I were you, I'll use an example for each one to remember them. And this one is for plurals: الجمع وأنواعه.
The infinitive, abstract noun or verbal noun (اسم الفعل or مصدر) of a form-I verb is not necessarily predictable. Many such verbs have multiple valid infinitives, and there are many cases in Lane's Arabic-English Lexicon where he notes the authorities differed on whether a given word was a true infinitive or a common substantive.
That said, there are some general rules that often hold true.
For transitive verbs of the measure فَعَلَ (fa‘ala) or فَعِلَ (fa‘ila), the infinitive is typically of the measure فَعْلٌ (fa‘lun).
For intransitive verbs of the measure فَعَلَ (fa‘ala), the infinitive is typically of the measure فُعُولٌ (fu‘oolun).
For intransitive verbs of the measure فَعِلَ (fa‘ila), the infinitive is typically of the measure فَعَلٌ (fa‘alun).
For verbs of the measure فَعُلَ (fa‘ula), the infinitive is typically of the measure فَعَالَةٌ (fa‘aalatun) or فُعُولَةٌ (fu‘oolatun).
And these are the five most common measures of the infinitive.
See Wright's Grammar of the Arabic Language, Vol. I, pp. 110-115, which contain the above information along with a more detailed analysis.