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

If a time-sensitive halachic question pertinent to one’s tefilla arises in the middle of Shemoneh Esrei, one may go to the place where the seforim are kept to search for an answer. If he is unsure of where the seforim are kept, he may go and look for a sefer. If he is unable to figure out the answer on his own, he may ask another person. If at all possible, he should write down the question, bearing in mind that he does not want his writing to be considered as if he is speaking.

סימן ק"ד ס"ק ב' ביאורים ומוספים דרשו 9 11

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

If a dangerous situation arises in the middle of Shemoneh Esrei, one should try to avoid the issue by walking away instead of interrupting his davening by speaking. Alternatively, if there is time before the situation turns dangerous, he can shorten his Shemoneh Esrei by reciting just the beginning and end of each brocha. Situations mentioned in halacha which are considered dangerous include: 1) a non-Jewish king or strongman coming to greet someone who is davening, 2) a scorpion or snake poised to attack a person during davening, and 3) a wagon or an animal such as an ox moving in his direction.

ס"ב-ס"ד ס"ק ד' ו' וי"א ביאורים ומוספים דרשו 13

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

Unless there is an important need, it is forbidden to step out of place in the middle of Shemoneh Esrei. If one did walk out of place, when he resumes davening he should continue from the last word he recited before he moved. In the middle of Elokai Netzor, however, one may walk out of place even if a slight mitzvah arises. For example, a chazan who does not take three steps back until after Kaddish may walk from his place in order to sit down during Tachanun. If one finished Elokai Netzor and said Yihyu L’rotzon, he may walk from his place even to do an action which is only perceived as a mitzvah, such as opening the Aron Kodesh for Avinu Malkeinu. After he finishes the task, he does not have to return to his place in order to take three steps back. 

ס"ב ס"ק ט' ביה"ל ד"ה אבל ביאורים ומוספים דרשו 20

• 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 tzibur is waiting for a distinguished person to finish Shemoneh Esreh 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.

• If someone is not davening directly behind a person 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.  

• Is it necessary to repeat Shemoneh Esrei if one pauses in the middle?

• Which brochos in Shemoneh Esrei are grouped together as one?

• Is one obligated to start over if he spoke in the middle of Shemoneh Esrei?