The verb form יושן is very controversial, in some linguistic communities it is very common, in others it is considered an abomination. In fact there is nothing wrong with it, but if you want to make sure that you not only are correct but you also sound correct to everyone, use ישן.
definitely the abomination. The יושן form is used as an imitation of baby talk. Don't use it at all.
The correct form of the present tense male singular or the verb root י-ש-נ is יָשֵן.
The rules that make it so are arcane, but it has to do with י being the first letter in the root. Most verbs, like the ש-מ-ר that is used for so many examples, have a different form of present male singular: שוֹמֵר.
So children who are not aware of the arcane rules and who haven't yet heard the correct form often enough form the word יוֹשֵן.
When adults use it, either they're extremely ignorant, or they're mimicking baby talk. A comparable English thing would be to say "all by my lonesome"
I think that "while" and "בזמן ש" are when stressing an activity that happened as a background to the action that's the focus of the sentence. It's almost necessarily a continuous action over a period of time, but it can be quite a short time: "While Bolt ran the 100 meters, I held my breath". Other than this special case, you can talk about very long period of time and use "when"/כש: "When dinosaurs walked over the earth, more of the earth was covered with trees."
Thanks. Very helpful. It's interesting to me that in some languages these constructions require taking into consideration mood, either the indicative or subjunctive mood in subordinate clauses when referring to the past (e.g., Latin "cum" clauses with the "sequence of tenses"), whereas Hebrew as a Semitic language has no subjunctive and so had to communicate matters such as mood, modality, and durative past action in subordinate clauses in other ways. Even though modern Israeli Hebrew as a revival language is famously influenced by European languages, particularly the use of participles, there are semantic and morphological restrictions on Hebrew borrowing from European languages. I think that the heavy use of particles, adverbs, and participles is Israeli Hebrew's way of trying to compensate for no subjunctive.