The Melachot of Shabbat

May I pull teeth on Shabbos? Does clipping fingernails on Shabbos involve a Torah prohibition? On Yom Tov, may I dig up earth to perform the mitzvah of kisuy hadam?

We set our Shabbat table with a larger "charger" plate under the main plate. At the end of the meal, we clear off the dirty dishes and leave the charger plates. Is there a problem with borer (selecting)?

Is there a way whereby a person suffering from angina or other heart disease may carry his medication on Shabbos through a public thoroughfare?

May I take a kugel that was on a hot plate on Shabbat and put it into a cholent that is in a crock pot?

A couple of weeks ago, we saw a mouse in the house and put out a cage trap. A mouse was trapped last Shabbat. Because we felt bad for the mouse, we took it (on Shabbat) to an isolated area and let it out. Did we violate anything by trapping the mouse on Shabbat, or by letting it out (like some melachot that come in pairs, like tying and untying)? Was the cage muktzeh and, if yes, did tza’ar ba’alei chayim justify taking it out?

A couple of weeks ago, we put out a cage mouse trap. A mouse was trapped last Shabbat. Are we aloud to set it out During Shabbat?

Is it permitted to remove loose hair on Shabbat, which usually includes ripping it, that has gotten stuck in a necklace?