Chatzi-Qaddish

As far as I understand, to be correct, the tzibbur should say בריך הוא * together * with the Baal-tfillah aloud, (not * after * the Baal-tfillah, repeating the phrase, as Litaim do)?

Similarly, for יתברך, it should be said * together * with the Baal-tfillah aloud?

Saying those words * together * with the Baal-tfillah is to underline that in those places, interruptions-hefsekim are forbidden?

Teimanim say Amen after יתברך and Amen after בריך הוא

Yekkes say we must answer Amen just three times during Chatzi-Qaddish (not five like Sefaradim)?

Why is it so crucial not to answer Amen in improper places, making interruption-hefsek, in Nusach-Ashkenaz?

Was the first "Amen" after יתגדל ויתקדש שמיה רבא planned by rishonim or appeared much later?
I have Artscroll-Siddur and there is no any first "Amen".
Maybe genuine Nusach was to say "Amen" just twice: before יהא שמיה רבא and in the very end of Chatzi-Qaddish?

Michael wrote: יתברך is a different issue - there is a ספק if יהא שמיה רבא goes on until יתברך (saying לעלם ולעלמי עלמיא יתברך), or is יתברך something completely separate, and יהא שמיה finishes at עלמיא.

It seems to me Teimanim don't have any ספק. They say יהא שמיה רבא and so on, then Shliach-Tzibbur says יתברך and all tzibbur say "Amen".
But Ashkenazzim have ספק?

The Artscroll Siddur may not say to say אמן, but every kehillah I have been with who oren from Artscroll say the first אמן after יתגדל... שמיה רבה. Furthermore, in their Madrich HaGabbayim, I believe that they say to say אמן (although they also include in brackets the additions for Nusach Sephard).

I don't know whose Minhag it is but Qitzur-Shulchan-Aruch by Shlomo Ganzfrid (Qaddish 15:5) also says when Chazan will say "Yitbarach" all tzibbur answer "Amen" (like Teimanim do too).
It seems to me Yekkes oppose this custom.
Why Yekkes consider it is very important not to say spare "Amenin"?