Can one take three steps back if the person behind him is davening Shemoneh Esrei?

As we have learned, it is forbidden to walk in front of a person who is davening Shemoneh Esrei. For the same reason, one may not take three steps back at the end of Shemoneh Esrei if someone behind him is still davening. The poskim disagree about whether this halacha applies in a case where the person behind him has completed Shemoneh Esrei but has not yet taken three steps back (he is also waiting for the person behind him to finish Shemoneh Esrei). If the person is not davening directly behind him but off to the side, the poskim disagree on whether it is permissible to take three steps back. Under pressing circumstances, one may be lenient. Alternatively, if there is a person davening directly behind him, he may take three steps back diagonally under pressing circumstances.  

סי' ק"ב ס"ה ס"ק י"ט ביאורים ומוספים דרשו 25 27

What is the proper way to deal with a disturbing child in the middle of Shemoneh Esrei?

It is forbidden to interrupt in the middle of Shemoneh Esrei even if a very important person is waiting for his greeting to be returned. Using hand motions is forbidden as well. In a case where a child is misbehaving and disturbing one’s kavanah, he may motion for the child to behave. If motioning is ineffective, he is permitted to walk away. If walking away is not an option, one may try to soothe the child without speaking. If the child is disturbing the other members of the shul or if he needs the bathroom, the father may interrupt his Shemoneh Esrei to escort the child out of shul.

סימן ק"ד ס"א ס"ק א' ביאורים ומוספים דרשו 2-3

What should a Rov do if he does not want the tzibur to wait for him to begin Shemoneh Esrei?

Motioning in the middle of Shemoneh Esrei is also permitted in the case of certain other disturbances. For example, if the tzibur is waiting for a distinguished person to finish Shemoneh Esrei in order to begin Chazoros Hashatz and he does not want them to wait (and his kavanah is being disturbed), he may gesture for them to begin. Likewise, if someone in the middle of Shemoneh Esrei sees that the person standing in front of him is waiting to take three steps back, and his kavanah is disturbed because he is inconveniencing his neighbor, he may motion for him to take three steps to the side. Similarly, if a person sees a child who needs help finding the place, he may gesture to show him the right place in the siddur.

ס"ק א' ביאורים ומסופים דרשו 1

• It is forbidden to sit within four amos of a person who is davening Shemoneh Esrei. Sitting while another person is davening gives the impression that one is uninterested in being mekabel ol malchus shamayim. If, however, the person who wishes to sit is also davening, he may sit next to the person who is davening Shemoneh Esrei.

• A weak person who does not have a place to sit outside the four amos of someone who is davening may sit within his four amos. He should not sit in front of him, however. 

• For the sake of certain mitzvos, walking in front of a person who is davening is permitted (e.g. to complete a minyan or to go up to duchen). The poskim disagree about whether it is permissible to walk in front of a person who is davening in order to wash hands for duchening.

• Is it permissible to ask a halachic question in the middle of davening?

• What is the best way to deal with a dangerous situation in the middle of davening?

• When is one permitted to walk around in the middle of Elokai Netzor?