By definition, Lubavitchers cannot be Zionists.

There were 3 or 4 branches of Chabad the last of which was Babroysk. R' Kook's mother was Babroysk as was the Rogatochver and R' Zevin.

The last rebbe of Babroysk, R' Shemarya Noach, passed away in '24 or so.

R' Zevin was a Zionist. How? Because he was not a Lubavitcher but a Babroysker.

Professor Marc Shapiro: "How could you be a Zionist if you are a Lubavitcher. By definition, Lubavitchers cannot be Zionists. Today they can be practical Zionists but they can't be religious Zionists. Can't think that the state of Israel is the beginning of the redemption or anything like that and Rav Zevin thought all that stuff. Hallel on Yom Atzmut and everything because he was a Babroysker. And he had a lot of respect for the Lubavitcher Rebbe Menachem Mendel Schneerson but he did not as they say mevatel himself. He did not put away his views. Because Babroyskers were independent." Lecture on R' Yechiel Michal Epstein #1.

1384 President Street

1384 President Street, Brooklyn, NY 11213

https://www.chabad.org/therebbe/livingtorah/player_cdo/aid/1023079/jewish/The-Rebbes-House.htm

pardes yosef

https://matzav.com/kever-of-pardes-yosef-discovered-in-lodz/

davening after 4th hour

Rabbi Yosef Avraham Heller, the Rosh Kollel of Crown Heights, Brooklyn and former member of the Beis Din there, wrote a essay explaining the Halachic justification for davening after Chatzos, published in "Kobetz Beis Chayenu" 11 Nissan 5760 pg. 28. The crunch of the explanation is as follows:

The Gemora (Brochos 26a) states that, "He may go on praying [Shachris] the whole day. But up to midday he is given the reward of saying the Tefillah in its proper time; thereafter he is given the reward of saying Tefillah, but not of saying Tefillah in its proper time." Although the mainstream view in Rishonim is that of the Rashba that after Chatzos is only considered tashlumim if he accidently missed the time, the Perisha in OC Siman 89 cites an alternative view that even after Chatzos is still considered the time of davening Shachris but only that one would not receive the reward for davening on time. Rabbi Heller continues to back up this view based on many Rishonim that maintain that the time for Shachris is the entire day. Although this Prisha argues with the Mechaber and Rama, Rabbi Heller suggest that since it concurs with the view of many Rishonim, Chassidim relied on his ruling in order to have adequate kavana in their davening.

There are also several letters of the Lubavitcher Rebbe on the topic collected in "Sharey Halacha U'Minhag" OC Chelek 1 pg. 111. The Rebbe brings the halacha (OC 98:2 and Rambam Hilchos Tefila 4:15-16) that proper kavanah during davening is integral to the davening, and without it the teffila is nullified. He asserts that therefore proper preparation for davening takes precedence over being exact in the time of davening.

However, it must be stressed that all the above is only when one is involved in davening or it's preparation from before zman tefila. There is no justification to begin davening after chatzos.

In terms of an opinion that as long as one begins before zman tefilla they may continue even after, I heard that this comes from Tosfos in Brochos 7a "Sh'ilmaley". The Gemora relates that Biliam tried to find the exact second Hashem was angry to curse the Jews, and Tosfos asks what he could have said in that short moment. In their second answer Tosfos says that as long as he would have started at a time of Divine anger the curse would work even after. Similarly, the "zman tefilla" follows when one begins even if he finishes after.

https://judaism.stackexchange.com/questions/22003/halachic-justification-to-not-pray-the-amidah-before-zman-tfilah

http://moshiachtalk.tripod.com/bikores/bikores00.htm

http://moshiachtalk.tripod.com/bikores/bikores00.htm

rebbe as moshiach

https://judaism.stackexchange.com/questions/38256/did-the-late-lubavicher-rebbe-consider-himself-a-to-be-a-prophet-and-or-the-mash

learning Chumash, saying Tehillim, and Learning Tanya daily

R' Zev Dov Slonim compiled a booklet that collates various sources that talk about the advantage of learning Chumash, saying Tehillim, and Learning Tanya daily. The booklet is also included in the Chitas sefer, published by Kehot. The footnotes on Sefer Haminhagim's entry on Chitas discusses this as well.

Here are some of them, see sources inside for more:

• The Shibolei HaLeket (Inyan Tefilla #44), brings from Rashi that the early Chassidim would learn for an hour after prayer. He connects this to the idea brought in the Talmud (Kiddushin 30A) , that one should always split his his learning into three. A third Mikrah, a third Mishna, and a third Talmud.
  Rabbi Slonim points out that in Shulchan Aruch HaRav (Hilchot Talmud Torah, Chapter 2, Halacha 1), the Baal HaTanya says that explanations of the Written Torah fall under the heading of "Mishna" and Kabbalah falls under the catagory of "Talmud".
  Hence, learning Chitas daily covers Mikrah (Tehillim, Chumash), Mishna (Rashi on Chumash), and Talmud (Tanya).

https://judaism.stackexchange.com/questions/17761/the-value-of-the-daily-study-of-chitas-chumash-tehilim-tanya/48064