Why do some people not wear a gartel?

Chazal teach that a person must adjust his clothing before davening Shemoneh Esrei. These preparations include tightening a belt or gartel around his waist. Even if a person already has a belt which separates between his heart and ervah, he must add another one to fulfill this halacha. Some poskim say that this obligation only applies to a person who conducts his daily activities while wearing such a belt; according to this view, wearing one regardless of whether it is part of one’s regular wardrobe is a midas chasidus. In many communities there is no custom to wear a gartel. The poskim explain that the reason for wearing a gartel before davening applied only in earlier times, when people commonly girded themselves before meeting important people.  Nonetheless, many communities adhere to the halacha in its original form.

סימן צ"א ס"ק ד' ביאורים ומוספים דרשו 5

May one greet a bareheaded person with the word Shalom?

It is forbidden to mention Hashem’s name bareheaded. Similarly, one may not walk into a beis hakneses without a head covering. If one did daven bareheaded, the poskim disagree about whether he has fulfilled his obligation b’dieved. The poskim discuss whether it is permissible to greet a bareheaded person with the word Shalom (a name of Hashem), as there is a concern that he may return the same greeting. Some are lenient, since the bareheaded person does not intend to use the word in reference to Hashem.

ס"ג ביאורים ומוספים דרשו 10

May one daven while wearing a Purim costume?

The poskim say that one must wear a hat and jacket for davening. Since this is the respectable way to walk outside and meet important people, one must do so when davening. If one does not have his hat and jacket and he will miss tefilah b’tzibur if he waits to get them, the poskim disagree about whether he should daven without them. They also disagree about whether one may wear his jacket over his shoulders during davening. A worker who is comfortable wearing his work clothes in the street may--under pressing circumstances--wear them for davening as well. On Purim, one may daven while wearing a costume as long as he is properly covered and he is not engaging in levity during davening.

ס"ו ביאורים ומוספים דרשו 16-17

• One should not daven in front of pictures or paintings. These images can disturb a person’s concentration. If disturbances arise, one should close his eyes when davening. Davening in front of a mirror is forbidden even if a person closes his eyes, since it gives the impression that one is bowing to his own reflection.

• A person may not daven next to, or in front of, his rebbi. It would be haughty to stand as an equal to the rebbi and certainly to stand in front of him. It is also forbidden to daven behind one’s rebbi.

• A talmid who is also a colleague has no restrictions regarding davening near his rebbi.

• Should one miss zman tefilah if he needs to relieve himself?

• Is a lecturer obligated to interrupt his shiur if he must relieve himself?

• May one interrupt between geulah and tefilah to use the restroom?