Drinking during Davening:
Once one has begun Baruch Sheamar, it is forbidden to drink until after Shemoneh Esrei [and Tachanun]. This prohibition applies even between the paragraphs [i.e. Bein Haperakim]. However, prior to Baruch Sheamar, and after Shemoneh Esrei [and Tachanun], it is permitted to recite a blessing over a drink.
Eating during Shacharis: It is forbidden to eat even before Davening, as explained in 89:5. Even those who are accustomed to eat a snack before Davening in order to have strength to Daven [see 89:5] may not eat beginning from Baruch Sheamar until after Shemoneh Esrei [and Tachanun], as stated above regarding drinking during Davening.
If one is very thirsty, or feels sick, and is having trouble concentrating in Davening, may he take a drink past Baruch Sheamar?
Some write that it is permitted to say a blessing on a drink, and drink it, in the event that one is very thirsty, or is sick, and as a result is experiencing difficulty in concentration. In such a case, it is best to delay the drinking until he is between the paragraphs [Bein Haperakim].
If one had a drink before Davening and did not yet recite an after blessing, may he drink during Davening, past Baruch Sheamar?
If one consciously had in mind not to conclude his drinking session upon beginning to Daven, and thus the Bracha Rishona that he said on the drink carries over, then seemingly it is permitted to drink even past Baruch Sheamar, being that he is not required to say a new blessing. However, some write that the actual act of drinking is itself an interval. Practically, this should not be done unless one is very thirsty, as stated above.
If one ate or drank before Davening and forgot to recite an after blessing, may he say it if he is past Baruch Sheamar?
Yes, as if he waits until after Davening, the time for which he can recite the after blessing may expire [Shiur Ikkul]. One is to recite the after blessing between the paragraphs [Bein Haperakim].
 Admur 493:17 regarding Besamim, that one may not say a blessing over it in Davening; So also rules regarding Besamim: M”A 494:9; Shelah Miseches Shavuos; Elya Raba 494:12; P”M 494 A”A 5; Kaf Hachaim 494:57
Other opinions: Some Poskim rule it is permitted to recite a blessing over Besamim, in between the Perakim of Pesukei Dezimra. [Chok Yaakov 494:7]
 As one is meant to recite Tachanun immediately after Shemoneh Esrei without making an interval. [Admur 131:1] Now, although in 493:17 Admur mentions between Baruch Sheamar and Shemoneh Esrei, and does not mention Tachanun, this is because it is dealing with the day of Shavuos in which Tachanun is not recited.
 The reason: As it is forbidden to make a speech interval and recite a blessing over the drink during Davening.
 Piskeiy Teshuvos 51:9; See Revivos Efraim 6:29 who brings Rabbanim who rule this way, although he does not give any conclusion of his own; See Vayivarech David 1:14
 The reasons behind this ruling: 1) We find regarding other intervals, that they are permitted to be made for the sake of concentration in Davening. 2) Admur ibid states regarding Besamim that since one is able to avoid intending to smell the smell of the Besamim, therefore, the blessing is not an obligation. Perhaps one can learn from here that if one cannot avoid the drink, such as due to being very thirsty, then since he may drink, he may also say a blessing over it.
 As in this event one also gains the opinion of the Chok Yaakov ibid who permits reciting a blessing over Besamim during Davening.
 However, in the event that one simply forgot to recite an after blessing prior to starting Baruch Sheamar, then seemingly it is considered Hesech Hadaas from the Bracha Rishona, as people are not accustomed to drink during Davening, and it is hence similar to one who said Shir Hamaalos before Bentching. Vetzaruch Iyun, as Shir Hamaalos concludes the meal while starting to Daven does not conclude the meal, as one may Daven in middle of a meal.
 So is implied from Admur and Poskim ibid regarding Besamim that only the actual blessing is an interval and not the act of taking the Besamim and smelling it and so would apply also to drinking.
 Piskeiy Teshuvos 51 footnote 86; Heard from Harav Yaakov Yosef Zatzal; See Beis Oved 51:3; Makor Chaim 51; Kaf Hachaim 51:17 that initially, one is not to make any interval during Davening, even if it does not involve speech, just as is the law regarding Shema.
 Piskeiy Teshuvos 51:10
 See Admur 184:3 and Ketzos Hashulchan 60 footnote 20 that one must recite an after blessing immediately after an un-filling meal due to suspicion that Shiur Ikkul would already pass.
 This is similar to any Mitzvah Overes, of which its blessing is permitted during Davening, until Shemoneh Esrei. [See Admur 66:4]
 As in this event one also gains the opinion of the Chok Yaakov ibid which permits reciting a blessing over Besamim during Davening.