Doing Activities Before Davening
In general, one should not begin an activity which will require of one to become engaged in it, before performing a mitzvah at hand. When it comes to davening specifically, there are unique stringencies and leniences for each of the davenings as detailed below.
- There is a positive aspect to learning before davening to prepare oneself for davening. 
- If one usually goes to daven in a minyan which is at a set time, then it is permissible to learn before davening even after Olot HaShachar and so, the minhag is to learn before davening. 
- It is permissible to learn until Olot HaShachar. However, once Olot Hashachar comes, it is forbidden to begin learning until one has prayed. Some are lenient to permit learning after Olot HaShachar until close to HaNetz HaChama. Nonetheless, it is permissible to learn even after Olot Hashachar in any of the following three circumstances:
- if one is learning in the place where a tzibbur will come to daven, 
- if one asked a friend who was not learning to remind one to daven before the latest time of Shema and Tefilla,  or
- if one was teaching Torah to a group or is learning in a group and if there is no concern that one will miss the latest time for Shema. 
- Some add that it is permissible if one is not learning in-depth. 
- If one already began learning before Olot HaShachar, one should continue and does not have to stop. If one began learning after Olot HaShachar, some say that one should stop for Kriyat Shema and some say that one does not have to stop as long as there is time prior to the latest time for Shema. 
- Someone who can not learn after Olot HaShachar and the tzibbur is only davening later, it is preferable for them to daven earlier and then learn even though one will not be davening together at the time of the tzibbur. 
- It is forbidden to do work after Olot HaShachar until one has prayed. From a half hour before Olot HaShachar it is preferable to say Birchot HaShachar before working.  However, work for a mitzvah is permissible 
- If one began working prior to Olot HaShachar it is permissible to continue afterwards. 
- One may take out the garbage on one's way to Shul before davening.
- It is permitted to do an activity which is a mitzvah before davening.  In some contexts, it may only be permitted if one can not do that mitzvah after davening and also that one should say Kriyat Shema before that activity. 
- It is forbidden to travel, beginning from Olot HaShachar until one davens. 
- Under extenuating circumstances--e.g. if one waits until after davening, one will not be able to travel, one will need to travel alone (which is dangerous), or there is a serious need for Parnasa (supporting a family)--one may be lenient, but one should first say Birchot HaShachar. 
- For the purposes of a mitzvah, one may travel before davening, but it is however preferable, to first say Birchot HaShachar.  E.g. if there is no minyan in the place one lives and there is a minyan in the place one is traveling to, or one will be able to have more concentration in the place one travels to. 
- If one stayed up all night, then it is forbidden to go to sleep within a half hour before Olot HaShachar until one has prayed. If one asks a friend who already slept that night to wake one up then it is permissible. If one can not ask a friend and one can not pray, one may be lenient and just say Kriyat Shema and then go to sleep. 
- If one was sleeping and woke up to go to the bathroom one may go back to sleep even after Olot HaShachar as long as one will not miss the latest time for Shema. 
- It is permissible to go to the bathhouse or cut one's hair until Olot HaShachar but afterwards one may not start to go to the bathhouse or cut one's hair.  However, a short shower with a little soap for someone who feels unclean in order to prepare for davening is permissible. 
- It is permissible to go to the mikveh after Olot HaShachar prior to praying 
- Prior to davening one should not pick up a child which may soil itself, or begin to cry when one puts it down and by the time one cleans up or appeases the child one may have missed the time for davening. 
- One should give tzedaka before praying.
- It is permissible to learn until Mincha Ketana (9½ hours into the day). However, once Mincha Ketana comes, it is forbidden to learn until one prays.  Nonetheless, under four circumstances it is permissible to learn even after Mincha Ketana:
- if one usually goes to daven in a tzibbur (minyan),
- if one is learning in the place where a tzibbur will come to daven,
- if one asked a friend who was not learning to remind one before the latest time of Mincha, or
- if one was teaching Torah to a group and if there is no concern that one will miss the latest time for Mincha. 
- From 9 hours in the day, one may not start work that could drag on and make one miss the time for Mincha. If one always goes to minyan and there is a set time, it is permissible, even after 9½ hours. 
Traveling, Showering, Shaving
- If one always goes to minyan and there is a set time, it is permissible to travel, shower, and shave, even after 9½ hours. 
- One should not sleep after 9½ hours. If one asks a friend to wake one up, then it is permissible. 
- It is permissible to learn until Tzet HaKochavim. However, once Tzet HaKochavim comes, it is forbidden to learn until one has prayed.  Nonetheless, under two circumstances it is permissible to learn even after Tzet HaKochavim:
Working, Traveling, Showering, Shaving
- If one always goes to minyan and there is a set time, it is permissible to work, travel, shower, and shave, even after Tzet HaKochavim. 
- One should not sleep within a half hour of Tzet HaChachavim. Asks a friend to wake one up only works at a time when people are not going to sleep and the friend is reliable. 
- Piskei Teshuvot 89:23. See there where he writes that the minhag is to be lenient to learn before davening because of the positive aspect of learning before davening.
- S”A 89:6, Piskei Teshuvot 89:23
- S”A 89:6
- Mishna Brurah 89:31
- Mishna Brurah 89:32
- Mishna Brurah 89:34. See the collolary to this for Kriyat Shema Arvit in Mishna Brurah 235:17.
- Shulchan Aruch 89:6 permits davening later if one is teaching a group. Mishna Brurah 89:35 says that this is only if there is no concern for missing Shema. Ishei Yisrael 13:34 in the name of Mekor Chaim 89:6 includes the case of learning in a group.
- Piskei Teshuvot 89:23 quoting Sh”t Avnei Tzedek 19 (however, see Mishna Brurah 89:33 who implies the opposite).
- Mishna Brurah 89:30
- Mishna Brurah 89:33
- Mishna Brurah 89:37, Ishei Yisrael 13:18
- Ishei Yisrael 13:19
- Mishna Brurah 70:23-5, Ishei Yisrael 13:22
- Rav Shlomo Zalman Auerbach (quoted by Tefillah Kehilchata c. 6, n. 36 and Ishei Yisrael c. 13, n. 46, p. 122) ruled that it is permitted to quickly look over a newspaper, take out the trash on one's way to Shul, or put a load of sorted laundry into the washer before davening. See also Eshel Avraham 89:3 who says that perhaps anything which is a quick and simple task which would be permitted on Chol HaMoed would be permitted before davening.
- Ishrei Yisrael (p. 122). A strong proof is: Rashi (Megillah 23a s.v. BeYom Tov), Mishna Brurah 529:14
- Mishna Brurah 250:1
- S”A 89:3
- Mishna Brurah 89:20, Ishei Yisrael 13:23. One should make sure that one is able to pray before the latest time nonetheless--Piskei Teshuvot 89:16
- Ishei Yisrael 13:24
- Piskei Teshuvot 89:16
- Piskei Teshuvot 89:22, Ishei Yisrael 13:31
- Ishei Yisrael 13:31
- Ishei Yisrael 13:31, Piskei Teshuvot 89:22
- S”A 89:7, Mishna Brurah 89:36
- Piskei Teshuvot 89:24
- Ishei Yisrael 13:21
- Halacha Brurah (Rav Dovid Yosef) 89:36, Avnei Yishfeh (pg 90) in name of Rav Vosner, Peninei Halacha (pg 162), and Piskei Teshuvot 89:24 are lenient for someone who regularly shaves. However, Sh”t Or Letzion (vol 2 7:9) and Halichot Shlomo (Tefilla 2:8) quotes Rav Shlomo Zalman Auerbach are strict under all circumstances and compare shaving to haircutting. Similarly, Yalkut Yosef (Tefillah pg 99, Siman 89:32) is strict but adds that those who do so regularly have what to rely on.
- Ishei Yisrael 13:37
- Kitzur Shulchan Aruch of Rav Mordechai Eliyahu 12:2
- Mishna Brurah 232:11 writes that the laws of learning before Mincha are the same as those for Shacharit after Olot HaShachar.
- Shulchan Aruch 89:6 with Mishna Brurah regarding Shacharit
- Mishna Brurah 232:9
- Piskei Teshuvot 232:3
- Piskei Teshuvot 232:3
- Ishei Yisreal 27:27
- Mishna Brurah 235:17
- Shaar HaTziyun 235:19
- Mishna Brurah 235:17 at the end
- Piskei Teshuvot 235:6
- Mishna Brurah 235:17
- Piskei Teshuvot 235:7