Halfon, let me disagree with you. מנסה and מנוסה are totally related. לנסות is "to try, to experiment". After trying or experimenting something many times, you are experienced.
Also משנה and משונה are related. לשנות is to change or alter something. Something משונה is, in my view, something that was changed or altered, and therefore unusual, weird, deviated from the norm.
Your translation משנה=matter is not accurate. It's true that coloquially we translate לא משנה=it doesn't matter but a more precise translation would be "it doesn't make a diference".
And because all the explained above, the roots are the same in both cases
I appreciate your comment, I checked it and you're right about the roots. But I still don't see direct connection between the words, I guess it depends on how you view it. for example משנה and משונה, when I change something it doesn't necessarily mean that it becomes weird, although it's possible and therefore I see indirect connection.
Is מנוסה related to מנסה? But if yes, how then the meanings of those two are related? In the same way, how משונה and משנה meanings are related? Because I'm thinking if I wanted to use a passive, it might turn out to be a completely different meaning! Thanks!
No. מנסה means "trying", while מנוסה means "experienced". They are not really related. Also משנה and משונה aren't related - משונה means "weird" "strange", while משנה means "matter". I'm an Hebrew native speaker, but my English isn't very good, hope you understand
edit- the word משנה can be used also as a verb with the meaning "he is changing" for example: הוא משנה את מיקומו mean "he is changing his position"
Yossi is pretty famous name in Israel, and yet I haven't seen any Yossi writing his name "Iosi". I've seen "Yosi" though