Is it appropriate to learn Torah at kivrei Tzadikim? (a) People seem to always be reading Tehillim there. So if this is the case, can they learn Torah Sh’be ketav there [e.g. Tanach]? (b) Can a person learn Torah Sh’bal peh there [e.g. gemorah and mishnayos]? (c) I noticed that the sefarim that certain tzadikim have written, with thier chidushim, have been put up for sale at the site, is it ok to read these there? (d) Is it mutar to sing while visiting the kevarim? I ask this because I have noticed that (i) people often times sing the verses of tehillim beautifully individually and also (ii) several times have seen people sing the verses beautifully in a group (e) Is it mutar to bring an instrument such as a guitar and play it while singing verses in Tehillim or Tnach or giving praises to Hashem? Recently I noticed a group of 3 individuals who did this, and it looked like one of them had a recorder in his hand. One was playing a small guitar, while all three were singing softly and quietly. It looked b’kovedic, sounded very nice, and their facial expressions were that of deveikus to Hashem. (f) At one kever, I noticed a sefer called “Shabbos Zemiros” on the book shelf. Assuming that no one is visiting the kevarim on Shabbos, I am assuming that it was placed there just in case someone wanted to sing shvach to Hashem. Is it mutar to sing non-tehillim praises to Hashem there (e.g. Bar Yochai, Dror Yikra, etc.)?
The reason I ask these questions is because, since a person who enters a cemetery is supposed to put there tzitzit in their pants, so as to give proper respect to those who have past, since they can no longer do mitzvos, then how does that differ from the examples given above (i.e. just as the deceased can no longer do the mitzvah of wearing tzitit, so too they can also no longer learn Torah Sh’b’ketav [e.g. recite tehillim], learn Tora Sh’bal peh, learn chidushim of other tzadikim, or sing shvach to Hashem whether from Tnach or not from Tnach)?
You are bringing up an interesting point. The reason we put our tzitzis inside when entering a cemetery of a place that has kevaim, is because it in a way is making fun of the deceased people there by showing thm that they can no longer do mitzvos, while we can. This is called “lo’eg l’rash” (lit. ridiculing the poor) The Shulchan Aruch writes that it is permitted to say tehillim, within 4 amos of a kever if it is for the benefit or the honor of the niftar, and it is not considered loeg l’rosh, as it is being done for them. This might be the reason why the monhag is to be lenient with this, and as you write, people, daven, learn, etc. at kevarim, as it is all included in the honor of the tzaddik.
שולחן ערוך יורה דעה סימן שמד סעיף יז מותר לומר פסוקים ודרשה לכבוד המת, בתוך ארבע אמותיו או בבית הקברות (מהרא”י בביאור מא”ח לדעת רמ”ה). וע’ שו”ת ר”י מגאש ס’ מ”ז, ושו”ת מנחת אלעזר ח”ג ס’ נ”ג, וס’ דרבי סופרים ס’ שס”ז ס”ק י”א.