Reb Eliezer

At the wedding, we make always a brocho on wine first. Maybe, because it generates simcha.
Similarly, this might be the reason that wine causes kiddush because it generates simcha, so we make the brocho on wine before the day as the Beis Hilel.

Off hand the connection here to אין עושין מצות חבילות do not pack multiple mitzvos on one time because it looks like you are burdened with it and you want to pater yourself off ASAP, does not make any sense. What connection does it have to the praising of Hashem with multiple items?` Maybe, it is talking in the case where he only mentions one thing in the end of the brocho but two things in the brocho. He wants to cover all the bases at once so, he is packing on multiple items to the brocho.

ברכות מט,ב

לעולם אל יוציא אדם את עצמו מן הכלל a person should not exclude himself from the group. This is the reason we always daven in plural. The Shunamis said מלכים ב פרק ד – וַתֹּ֕אמֶר בְּת֥וֹךְ עַמִּ֖י אָנֹכִ֥י יֹשָֽׁבֶת: I don’t want to separate myself from the group because then I become individually responsible for my actions. The Rabbenu Bachaye in Parshes Ki Siso explains שמות פרק ל פסוק יב – וְלֹא־יִהְיֶ֥ה בָהֶ֛ם נֶ֖גֶף בִּפְקֹ֥ד אֹתָֽם: no plague should occur when counting them. Together we are all tzadikim, but we get separated by counting and the bad will be revealed.
The Midrash Shmuel explains the mishna in Avos where Hilel says משנה מסכת אבות פרק ב משנה ד – הלל אומר אל תפרוש מן הצבור don’t separate yourself from the group, if you think you are better than they are, then don’t trust yourself until the day of your death, if you think the group is not as good as you are, don’t judge them until you arrive in their place, if you think they don’t want to listen to you, don’t say something which is not worth listening to, if you think you will join later, then think that maybe you will never have time to join.

ברכות מט,א

The Sefer Amudeho Shivo explains why we say Alenu after a bris. Simply we say יוצר בראשית to remember that Hashem created the world for the Jews sake and the bris differentiates us from the goyim. He gives an interesting reason. As we see that the kosher animals are physically different than the non- kosher, so why shouldn’t the Jews be born physically different than the goyim? Then, we would say their are two reshuyos, two deities on for tor the Jews and one for the goyim. Therefore, a bris is a proof for having One G-d, so we say Alenu to substantiate the Uniqueness of Hashem.

ברכות מח,ב

When including someone in betching, there is a difference between the one mezuman betching and one just included. The one bentching must eat at least a kezayis grain whereas the one included only needs to eat or drink something.
There is an argument in SA O’CH 186,1 if women are obligated biblically or rabinically in bentching, see Tosfas above 20,2. The question will be if a man can be yotzei with their bentching. They did not inherit land on their own and whether they have an obligatiion to learn Torah and say bichas Hatorah. Since they must know theiir mitzvos, so they make the brocho, SA O’CH 47,1The MAsaysnthatn. Bris not having is like having it otherwise how was Tzipora able to cimcumcise her son.

ברכות מח,א

Tosfas says that holding a chumash is foolish and does not help but holding a sefer torah might, the RMA SA O’CH 55,4 is lenient with a chumash in case of need. Maybe, they wanted us to realize that we don’t include everyone so easily into a minyan even for the tenth.
When it comes to davenen only six must daven but by bentching seven is required a recognizable majority because bentching is biblical whereas davenen is rabinical.

ברכות מז,ב

When they sold Yosef, Hashem was included in the Beis Din. Rebbi Akiva, a descendent of gerim, was included in the ten martyrs in place of Him. In SA O’CH 55,4 questions whether a katan can be included with a chumash as a slave was included and one freed. The Rosh says that he was needed for Parshas Zachor leinen which is biblical. In Europe a katan was included with a chumash. The Taz says that one speaking in the middle of davening should not be included in a minyan.
The Chacham Tzvi 93, questiions if a golem can be included. He brings a proof from Maseches Sanhedrin 65
where Rava created a golem and brought in front of Rebbi Zeira who said he has no use for it and destroyed it. It cannot speak and has no soul to become part of a minyan even though someone asleep can be included.

Amen chatufeh according the SA above, not the answer Amen before the brocho is finished.
It says one who follows the stringencies of both the Beis Shamai and Beis Hilel on him it is writtenl כסיל בחשך הולך the fool walks in darkness. The Ostroptzer in Sefer Meir EIn Chachomim explains this in an interesting fashion.
According to the Beis Shama whoi holds shevisas kelim, the pots and candle holder have to rest on shabbos, asks the gemora, how can one light shabbos candles? TThe gemora in Maseches Shabbos answers that he is mafker it. However, if he folows the Beis Shabbai view of shevisas kelim and the Beis Hilel’s view that hefkar has to be complete, both for the poor and the rich, so when he lights candles he regains some ownership, so hafker will not work and therefore will stay in the dark.

ברכות מו,ב

There is an argument in SA O’CH 165,2 who should wash his hands first. The SA says the geatest but the Rosh says that smallest in order the greatest should not have to wait without being able to talk. By mayim achronim we start from the smallest in order of sitting. MB O’CH 181 s’k 13.