If a person wakes up but is not sure if what came out of his body is a tiny amount of semen or not. Is he permitted to read the Tanach or study Torah before becoming pure again on the evening?
Rambam, Laws of Reading the Shema 4:8
ח כל הטמאים--חייבין בקריאת שמע, ומברכין לפניה ולאחריה והן בטומאתן, אף על פי שאפשר להן לעלות מטומאתן בו ביום, כגון הנוגעים בשרץ או בנידה וזבה ומשכבן וכיוצא בהן. ועזרא ובית דינו תיקנו שלא יקרא בעל קרי לבדו משאר הטמאים, עד שיטבול; ולא פשטה תקנה זו בכל ישראל, ולא היה כוח לרוב הציבור לעמוד בה--לפיכך בטלה. וכבר נהגו כל ישראל לקרות בתורה ולקרות קרית שמע, והן בעלי קראין, לפי שאין דברי תורה מקבלין טומאה, אלא עומדין בטהרתן לעולם.
Anyone impure is still obligated to recite the Shema with its blessings, even if they could become pure again that same day, such as those who touched a dead creepy-crawly, a regular or off-cycle menstruant or their bedding, and the like. Now Ezra and his court decreed specifically regarding a man with seminal emissions, vs. all other categories of impure people, not to recite Shema until immersing in a mikvah; however this enactment never spread throughout the Jewish people and the majority of the community could not keep it, therefore it became void. It has thus become the standard practice among the entire Jewish people to read the Torah or recite Shema despite seminal emissions -- the words of Torah can't become contaminated, they remain eternally pure.
There are those in the Hassidic world who go to the mikvah every morning, in deference to Ezra's enactment. (And then they could say Shema or Torah immediately after immersing, even though technically they're not tahor until nightfall.) A twist on this would be that a ten-minute shower would likely also suffice -- there were leniencies in Ezra's enactment to include water that had been in a storage tank. But fundamentally we follow Rambam's language: Ezra's rule never stuck, and we study Torah irrespective of ritual-purity status.
I feel obligated to point out that some who have tried to be extra-stringent (if it wasn't their communal norm) about the Ezra thing have spiraled down into OCD. So please check with a good rabbi before trying it.
Basically yes. (Rambam, Kriat Shema, 4 8) Though, there is a lot more to add regarding this (see comments)