Seforim must be double covered in bedroom to have relations. A garment draped over a cabinet of books is considered a double covering. But a Sefer Torah is so holy that a full mechitza is necessary, and if possible, it really should be moved out of the room.

Person should distance 4 amos from excrement and urine b4 Shema, and if it's still in front of him, he should really make sure it's not in his vision. However, regarding a bathroom that has been designated but not yet used, one can pray even within the line of vision.

We learned that a Ba'al Keri should immerse b4 studying Torah. If he has an additional Tumah and therefore immersion will anyways purify him completely, we have a dispute between Rabbis and R' Yehuda. The Rabbis still require immersion to at least rid the person of Keri and allow him to study Torah, but R' Yehuda says he will anyways be tamei there is no requirement to go to the mikvah b4 studying Torah. R' Yehuda says this leniency regardless of whether the Keri came before the other tumah.

Shachris can be fulfilled until midday. R' Yehuda says until 4 hours into the day. Mincah is until evening. R" Yehuda says until play hamincha. Mussaf can be the entire day. R' Yehuda says only until 7 hours into the day.

Even though the mishna says latest time for schachris is midday, that is for tefiillah in its time, but there is also a makeup time for those who missed the shcahris to pray an additional mincha.

The Gemara wonders is one missed mincha, can there be a makeup prayer at night by Maariv or do makeups only work within the same day itself. We rule that there could be a makeup prayer.

There is no makeup for someone who intentionally missed davening.

If one missed friday mincha, they daven 2 marrivs of Shabbos. If one missed shabbos mincha, they daven 2 weekday marries. Havdalah should be made in the first and not the second. If one made havdalah in the second and not the first, the 2nd one counts for maariv and he must daven a 3rd for the makeup.

Tefillos were instituted either bc the Avos set them up. Or bc they are associated with the offerings brought in the Temple.

R" Yehuda's plag hamincha time is 10 3/4 into the day, or an hour and a quarter b4 the end of the day.