בעלמא די ברא כרעותיה (בנוסח הקדיש)
The basic understanding of this phrase is that the world was created according to His Will. However, the word כרעותיה (translated as (כרצונו seems to be extra, since certainly when G-d created He did so according to His Will (nothing else existed).
It is possible to explain according to what Rashi wrote (Bereshis 1,26 נעשה אדם) that during the creation of Man, HaShem (as if to say) consulted with the angels and thus, a plural is applied to this creation. This is understood that when one consults with another about a decision, one does not make the decision by oneself, but the decision becomes a joint product of the consultation.
We already know that the angels were created on the second day. Thus, on day one nothing was created with whom HaShem could consult. Thus, HaShem created in the beginning only according to His Will. And thus, in the words of the Kaddish, reference is made to the initial creation which was only done by HaShem, as opposed to the later creation of man in which the angels were involved.
מבדיל בין יום ובין הלילה (בתפילת ערבית)
At first the prayer states “He causes the day to pass and brings on the night”, then the additional phrase that “He separates the day and the night” seems to be an unnecessary repetition of the same concept.
The phrase expresses the strength of the Creator that He set the daily patterns in a faithful manner. This is similar to the concept expressed by the Medrash that “flesh and blood” do not know the exact times that day ends and night begins, and thus, we need to add from the sacred to the holy (at the beginning of Shabbos). However, HaShem knows the exact time to distinguish between day and night, and can begin Shabbos at the exact correct moment.
Thus, we praise G-d at night that He established the daily patterns and knows them exactly. Thus, we use the phrase מעביר יום (causes the day to pass) since HaShem knows exactly when night occurs and the day has passed.
חמדת ימים אותו קראת (בתפילת שמו"ע של שבת שחרית)
We do not find an explicit place that HaShem calls Shabbos the most desirable of days.
However, the Targum Yerushalmi translates the verse (Bereshis 2,2) “and G-d completed (ויכל) on the seventh day” as וחמיד ה'. Thus, the concept is that HaShem “desired” on the Shabbos. This is similar to the verse in Tehillim (119, 81) כלתה לתשועתך נפשי, and other places. Thus, we find in many places that HaShem “desires” items (such as the Jews, Eretz Yisrael, etc.) Certainly, the day of Shabbos is beloved to HaShem, since He blessed and sanctified the day.
