May one change the direction he is facing in the middle of Shemoneh Esrei?

A person living in Chutz L’Aretz must turn towards Eretz Yisroel when he davens Shemoneh Esrei. If he is already in Eretz Yisroel he must turn towards Yerushalayim, and if he is in Yerushalayim he must turn towards the place of the Beis Hamikdosh. Before he begins, he must imagine that he is standing in the Beis Hamikdosh in the Kodesh Hakedoshim. If one began Shemoneh Esrei facing the wrong direction, he should not move his feet to change direction. Instead, he should turn his head in the appropriate direction. If he is in shul together with a minyan, however, he may turn to face the same direction as the rest of the tzibur. 

סימן צ"ד ס"ק א' ג' וי' ביאורים ומוספים דרשו 1

Which direction should one face when he davens for wisdom?

The Gemara teaches that one who wishes to be wise should daven facing southward and one who wishes to be wealthy should face northward. To simultaneously fulfill the halacha of davening in the direction of Eretz Yisroel, some Rishonim say that one should turn his head towards Eretz Yisroel. Others say that one should always daven facing  Eretz Yisroel and should turn his head northward or southward in alignment with his wishes for wisdom or wealth. The custom is to follow this view so that one will not stand out from the rest of the tzibur. The poskim say that it is not necessary to face northward or southward for the entire davening. Instead, at the time that one is davening for wealth he should face northward and when he is requesting wisdom he should face southward.  

ס"ב ס"ק י"ב ביאורים ומוספים דרשו 8

Where should the Rov sit in shul?

In countries west of Eretz Yisroel, the appropriate direction to daven is eastward. Since the tzibur davens facing east, it is customary to position the Aron Kodesh along the eastern wall. If this is impractical, the Aron should be built along the southern wall. Either way, the proper way to daven is eastward. Since many European countries are northwest of Eretz Yisroel, many poskim hold that the proper direction to face is southeast. Some communities, however, maintain the original custom of facing directly eastward. In those shuls, the Rov should be seated to the north of the Aron Kodesh so that he can face southward to pray for wisdom. In a shul which faces southeast, the Rov’s place should be to the right of the Aron.

ס"ב ס"ק ט' י"א

• It is not proper to collect tzedakah during Kriyas HaTorah, Chazoras Hashatz or Kriyas Shema. One who is in the middle of davening is exempt from giving tzedakah since he is involved in another mitzvah. He may choose to give if he wants to.

• It is appropriate to enter into tefilah in a state of fear and humbleness. Since it is difficult for the average person to reach this level before davening, one should try to connect instead to the happiness which comes from doing a mitzvah.

• In earlier times, pious people would meditate an hour before, and an hour after, davening. Meditating before davening is beneficial for kavanah and meditating afterwards shows that tefilah is not a burden. 

• May one daven Shemoneh Esrei on a city bus?

• Should an airplane passenger stand for Shemoneh Esrei?

• Can one lean during Shemoneh Esrei?