You may kill mosquitoes and other insects on Shabbat if they carry deadly diseases (which makes the insects a danger, or sakana). You may kill insects that might carry deadly diseases even if you do not know for certain that they do.

You may kill mosquitoes and other insects on Jewish festivals if they carry deadly diseases, which makes the insects a danger (sakana). You may kill insects that might carry diseases even if you do not know for certain.

You should not do laundry on chol ha'moed.

You should not shave or cut your hair on chol ha'moed.
Reason Chazal made a takana so people would do those types of grooming before each holiday and not wait until chol ha'moed.

All Jews, both men and women, must fulfill the commandment to remember what Amaleik did to the Israelites. The paragraph about that episode, called Parashat Zachor (found in Parashat Ki Teitzei:  Deuteronomy/Devarim 25:17-19) is read on the Shabbat morning before Purim as a law established by Chazal (takana). The commandment is fulfilled whenever that episode in the Torah is read, even privately and at home, but there is special value in hearing it read in a synagogue on that Shabbat preceding Purim.

Cheese/Gvinas Akum
 
Gvinas akum is cheese which has been made by non-Jews and by rabbinical prohibition is only kosher if a Jew was present during the cheese making OR if a Jew put the rennet into the milk.
Note If a Jew owns the milk before processing, a non-Jew can add kosher rennet as long as it can be confirmed that the rennet is kosher, even if no Jew is present during the cheese making.
 
Origin of the Problem: Chazal were concerned that the rennet used to make cheese might be from a non-kosher animal or even from a kosher animal that had not been slaughtered properly. Shulchan aruch says that even cheese curdled by kosher plant enzymes (such as fig branch sap or substances from certain thistle plants) are subject to the takana.
Note Gvinas Akum is not related to chalav yisrael; they are separate halachot.

Note Even rennet-less cheeses need hashgacha (religious supervision), but some non-hard cheeses may be an exception. Ask a rabbi.

Gender/Kashrut Status Transfer
Foods and kitchenware (pots, pans, dishes, utensils, and containers) can absorb taste from each other and so adopt a new gender or kosher status. They can change from:

• Kosher to non-kosher,
• Kosher pareve (neutral) to kosher dairy or kosher meat, or
• Kosher Passover to kosher (or non-kosher) non-Passover.

 
Note You can sometimes change a utensil/container to kosher-pareve (see Kashering, below), but you cannot change a

• Gendered food to neutral-pareve, or
• Non-kosher food to kosher.

 
Taste Absorption
Taste gets absorbed in three ways: Heat, pressure, and soaking. 
 
Heat
To absorb taste, and therefore gender or kashrut status, through heat, a food or utensil must be heated to 120° F or more while:

• Steamed with a halachically “liquid” food, or
• In wet physical contact with the food or utensil.

Examples

• Two hot pans, which are clean on their outsides, only transfer taste from one to the other if they are wet on the outside and are touching each other.
• A hot utensil placed onto a counter only transfers gender to the countertop if there is liquid or food at the point of contact.

Note  All liquids plays a major role in facilitating taste transfer.
NOTE Taste, gender, or non-kosher status do not travel upstream into the utensil that food is being poured from. Even if you pour hot liquid (pareve or of one gender) from a pot onto a non-kosher or opposite gender food, the genders are not transferred back through the stream of liquid to the pot, even if any or all of the elements are more than 120 degrees.
Situation You pour hot liquid from some pareve vegetables into a non-kosher sink that had hot in it within 24 hours. There are dishes or utensils in the sink.
Status The dishes do not change gender unless the hot liquid fills up from the sink onto them. If so, the dishes or utensils become non-kosher. But no gender change occurs through the stream of liquid back to the pot of vegetables.
 
Note If the non-kosher sink had not had anything hot (120 degrees or above) in it for at least 24 hours, no change of gender or kosher status happens at all.
 
Note On Passover, gender and chametz status DO get transferred through a stream of hot liquid.
 
Pressure
To absorb taste, and therefore gender or kashrut status, through pressure or short-term soaking, one of the items must be spicy/charif.
 
Soaking
To absorb taste, and therefore gender or kashrut status, through long-term soaking, the food must soak for specific amounts of time.
 
Note If the food or utensil is not hot (120° F or more), is not spicy/charif, and is not soaking for a long time, there is no gender or kashrut-status transfer.
Examples
You may use a non-kosher utensil for any cold food of the opposite gender, so you may:

• Eat cold (kosher) cereal out of a meat or non-kosher bowl, or
• Use a meat or non-kosher spoon to eat kosher ice cream.

Note Even though these are permissible, they may not be done regularly but only on an ad hoc basis.
 
Food and Kitchenware: Which Influences What
Hot or Spicy/Charif Foods
With hot (more than 120° F) or spicy/charif foods:
Foods and utensils/containers transfer taste to each other.
 
Cold or Non-Spicy Foods that Soak
With cold (less than 120° F) or non-spicy/charif foods that soak:

• Foods do not transfer taste to utensils/containers;
• Utensils/containers do NOT transfer taste to foods.

NOTE No substances (not salt, or any food...) absorb gender from the open air.
 
 
The 24-Hour Rule: Eino ben Yomo
Torah Law: Reverts to Kosher-Pareve
By Torah law, a utensil/container always reverts to kosher-pareve after 24 hours (since the taste of any absorbed food becomes ruined with time). 
 
Rabbinic Law: Must Be Kashered
However, by rabbinic law, the utensil/container must be kashered before using.
 
NOTE Even by Torah law, a hot or spicy/charif food can revive the milk-meat or non-kosher status of another utensil/container (see below) even after 24 hours.
 
Accidentally or Intentionally
Food Hot and Accidentally Placed; Utensil Not Hot for 24 Hours
Kosher food hotter than 120° F (49° C) remains kosher if accidentally placed into a non-kosher, clean utensil that has not been heated to 120° F or more for at least 24 hours.
REASON After 24 hours, b'di'avad, the utensil has reverted to being kosher-pareve.
NOTE If the utensil had been “used” (heated to 120° F or more) within the preceding 24 hours, the hot food that accidentally entered the utensil would be non-kosher. Ask a rabbi for possible exceptions.
 
Food Hot and Intentionally Placed
If the hot food had been put into the utensil intentionally, the food would not be kosher.
REASON Chazal made a rule (takana) that if you intentionally place food of one gender into a utensil of the opposite gender and heat it to 120° F or more, the food is not kosher.