1) The root of the word Sudni lies in the word "Sod" -- "secret." This is clearly seen from definition b and c, which both Rashi and the Aruch (that you quoted above) learn from the Pasuk of "Sod Hash-m l'Yerai'av" -- "The secret of Hash-m is to those who fear Him" (Tehilim 25:16).

The Gemara in Pesachim (113a) tells us that this is also why Sudni was the name for a beermaker. Asking why a beermaker is called a Sudni, the Gemara there quotes Rav Chisda who explains: "It is a nice secret and involves kindness." What does this mean? The RASHBAM (DH "Sod Naeh" "u'Gemilus Chasadim") explains that it is good advice, as one gets rich from it. Why does it involve Chesed? He explains that as a person can make a large batch of beer without having to spend a lot of money, he can easily afford to give some to the poor as well. It would seem that when the Rashbam said that one gets rich from it, he was also referring to the fact that it is cheap to make, making it a high profit item.

The common denominator between all three definitions is indeed a "secret."

2) I think that you are referring to Tosfos on 44b (DH "Avidna"), as the Gemara you quoted is in fact in Eiruvin (96a) and mentioned in our Tosfos (the Gemara in Berachos does not mention the teaching from the Pasuk, but does mention that the people in Eretz Yisrael used to say a Berachah of "Lishmor Chukav" when they took off their Tefilin). I am unsure whether you are asking how this is derived from the Pasuk of "Chukah," or why there is such a prohibition. I will therefore address both questions.

This Halachah is derived from the Pasuk of Chukah because the Pasuk is mentioned when the Torah discusses Tefilin (Shemos 13:10). The next words of the Pasuk are "mi'Yamim Yamimah" -- "from days all days," which some Tanaim understand as teaching us that one should only wear Tefilin during the day, and not at night.

A possible reason for this Halachah (though there are always many reasons for a Halachah) is that Tefilin are supposed to be worn as much as possible and, in the time of the Gemara, were in fact worn by many people throughout the day. Being that one is not allowed to take his mind off of his Tefilin (see Yoma 7b) or sleep a permanent sleep in his Tefilin (see Sukah 26a), it is reasonable that the Mitzvah would not be given at night, when people tend to go to sleep. There is in fact an opinion brought in Menachos (36b) which says that one can wear Tefilin at night, until the time when people go to sleep. This shows that falling asleep with Tefilin is a concern, which might be the reason that the Mitvza would not be given at night.

Take Care,

Yaakov Montrose