During “Elokai,netzor….”, one may answer as if in the middle of shema or its berachos–answering barchu; kadosh..and baruch (of kedusha ); amein of hokail hakodosh and of shome’a tefilah; amein, “yehei shemei” and da’amiran b’alma..(in kaddish); the first three words of modim derabbanan; and the three ameins of birkas kohanim.
If possible, yiheyu leratzon…should first be said.
One may not do any work or activity of a secular nature in a Shul or a Beis Medrash. For the purpose of fixing or repairing something of the Shul, it is muttar, though even then it is better, if possible, to do the work outside the Shul.