Q: Should one daven at the Kotel while facing straight ahead or turn to the left, towards the spot of the Temple?
A: Straight, since the exact location of the Holy of Holies is unknown (Le-Mikdashech Tuv p. 241. Shut Teshuvot Ve-Hanhagot 3:39. And this is what we heard from Ha-Rav Neventzal and Ha-Rav Simcha Ha-Cohain Kook).
Back to the Kotel
Q: Is it permissible to turn one's back to the Kotel?
A: It is permissible just as in a shul it is permissible to turn one's back to the Torah ark. When one leaves the Kotel, the custom is to walk backwards with his face towards the Kotel until he reaches the Plaza (This was the custom of the Steipler. Orchot Rabbenu vol. 1 p. 320 and vol. 2 pp. 150-151. And also Ha-Rav Neventzal, although Ha-Rav Shlomo Zalman Auerbach was not particular to do so. Ha-Kotel Ha-Ma'aravi – Halachot U-Minhagim p. 40).
The Kotel's Plants
Q: Is it permissible to trim the plants on the Kotel?
A: There are those who are strict with regards to them, since perhaps they have the same holiness as the Kotel (see the book "The Chief Rabbinate of Israel – 70 Years since its Establishment" vol. 2 p. 774, which discusses the dispute between the Chief Rabbis whether it is permissible to cut the plants which grow between the stones of the Kotel. Ha-Rav Ovadiah Yosef rules that it is permissible if an engineer establishes that they endanger the Kotel. But Ha-Rav Shlomo Goren was opposed, based on the idea that "the growth symbolizes the destruction," as is found in Megillah 28a-b. See too Shulchan Aruch, Orach Chaim 151:1, that Shuls in a destroyed state should be left alone and the growth in them should not be cut. This is in order to heighten one's anguish. Ha-Rav Goren also notes that the Kotel has stood for thousands of years without the growth being cut).
Tearing one's Garment at the Kotel
Q: Do I have to tear my garment when I visit the Kotel after a long time?
A: We do not tear at all since it is under Jewish sovereignty (Tal Chermon – Moadim, p. 218).
40 Days at the Kotel
Q: What is the source for the idea that if one prays 40 days straight at the Kotel, his prayer will be answered?
A: There is no source. This is a new creation. Any prayer, even one time, is heard. There are, however, various sources about the value of prayer for 40 days based on Noach in the ark and Moshe Rabbenu on Mt. Sinai. But every prayer is heard, and there is no need for forty days of prayer (see Ha-Rav Yosef Shalom Elyashiv in "Ha-Shakdan" vol. 2 p. 109).
Holiness of the Kotel's Stones
Q: Is it permissible to place one's fingers in the cracks and crevices of the Kotel?
A: The book "Mishkenot Le-Avir Yaakov" forbids it since it is forbidden to enter the Temple Mount when impure and the Kotel is considered part of the Temple Mount (chapter one of Massechet Tamid). Many authorities are therefore strict in this matter (Ha-Rav Joseph Soloveitchik in Nefesh Ha-Rav p. 101 and the Chazon Ish in Pe'er Ha-Dor vol. 2 p. 48). But the Avnei Nezer (vol. 2 Yoreh Deah 450-451) permits it because the Kotel does not possess the holiness of the Temple Mount, and even if we say that the Kotel is part of the Temple Mount, entering with one's fingers is a "Bi'ah Bemiktzat" (a partial entrance) and is not considered entering; and even if we say that a "Bi'ah Bemiktzat" is considered entering, it is not entering in the usual manner, since people enter through the gates and not through the walls. And this is the ruling of many authorities (Ha-Rav Ovadiah Yosef in Ha-Kotel Ha-Ma'aravi Halachot U-Minhagim pp. 74-75 note 47 and Ha-Rav Shlomo Zalman Auerbach said that the great Rabbis of Israel were not concerned about this). But it is proper to be strict. And our Rabbi, Ha-Rav Tzvi Yehudah, was careful not to place his fingers between the stones of the Kotel and refrained from kissing a stone of the Kotel which was not protruding.
Notes in the Kotel
Q: Is it permissible to place notes in the Kotel?
A: One should daven directly to Hashem. He does not need notes (When a Torah scholar mentioned to our Rabbi the custom of placing notes in the Kotel, our Rabbi said that one should not do this, and one should even refrain from putting one’s fingers into the Kotel [since it is forbidden for an impure person to enter the air of the Temple Mount in even the slightest way]. The Torah scholar said to him, “but this is the custom of Israel [minhag Yisrael].” Our Rabbi responded, the word "minhag" [custom] contains the same letters as "gehinom" [purgatory]. Le-Mikdashech Tuv, pp. 12-13).