In general there are 3 ways of coming close to God: most common, either through emotion or intellect, but then Judaism adds: or to be "similar" [=close] to Him. The greatest gift that He could give us is the "Tzelem Elohim", or capability of imitateo dei, being Godly. The she'ur discusses the advantages & disadvantages of each approach to Him. Most importantly, we can't understand His Essence, but we can amd should understand His actions. This is the ultimate in both the Rambam's rational and also the kabbalistic approach to Judaism. Rav Kook explains that the 13 traits of God, as well as the 10 sfirot, all detailus what to emulate. This has far-reaching ramifications for prayer, study as well as defining our goal and potential in life!
When Jerusalem is built in her glory, and even already today, it's the religious, national and universal capitol of Israel. God placed the "checks and balance" system, comprised by this Triumvirate of the king (national leader), Nasi haSenhedrin (religious leader) and Kohen Gadol ("Lover of Peace"- the humanist/universal leader) on one mountain forcing them to unite and work together. Rav Kook analyzes that all human ideologies are either right-wing (natl.), left (humanist), or religious (all the above are religious, but here, in the limited sense), who are all necessary, and also limit each other from going extreme. As long as each stress the positive & compliments the others, and isn't "anti", we will reveal the Unity of God and Israel.
If one answers an inquiry about what day of the omer it is and does not count again that day, may he count the next day with a beracha? If yes, an onen (before funeral of close relative, who does not perform mitzvot) for a full day of sefira should be able to simulate such a statement and be allowed to continue with a beracha the next day.
Why is the mourning period for the students of R. Akiva, so much more halachically serious than similar tragedies, in Jewish history? The class deals with the historic background of the time, as seen in the sources and archeology, which explicitly prove that the tannaim, R. Akiva's students, learned in a "Hesder" Yeshiva, combining Torah study with army service. They didn't wait passively for the redemption, but actively tried bringing it in the religious-Zionist way, which in their time was premature, but nevertheless serves as the Rambam's precedent for the future geula. Many other "innocent" sources in the Talmud are explained here, on the backdrop of the historic events of their time, and show that the Omer period mourns the fall of the 3rd State of Israel, a true national tragedy.