According to this page, きく means to pay attention to something with an intention to receive, or perceive, something that is produced from it. This process includes waiting till that thing is delivered and understanding its meaning.
It is also used, intransitively, to mean someone possesses an ability to perform such an act, or by extension, something ...
Are they used by older people/in formal situations?
This depends on the word. Some are old enough and safe in business settings (e.g., メモる, トラブる, サボる). Some are rare and/or slangy. They are generally avoided in very formal legal documents, etc.
Are they really slang?
Generally yes, but many are widely used in day-to-day business settings, and there are ...
My major is not linguistics but I found some interesting references for you.
Aoki introduces a few types of classification of transitive/intransitive verbs in Japanese.
The first classification is written by Kuginuki. It says there are 3 patterns of transitive/intransitive verb pairs.
Depending on the type of conjugation (第Ⅰ群形式)
知る (四段活用 is an ...
Assuming you are not asking for the historical origin, the uncontracted form of 'っこない' is 'ことはない'. Your sentence becomes お前には分かることはないでしょう
こと means here something like event or situation, so ' V + ことはない' (more) literally means that the situation where V happens is impossible. Hence, the construction means 'there is no way ...', as you already see.
I found several people who think らぐ is some kind of suffix, but looks like this is not explicitly listed in dictionaries as a standalone suffix. If らぐ is a suffix, it should be similar in purpose to English -ate used to turn words into verbs (e.g., formulate, activate).