כרר

Abarim Publications' online Biblical Hebrew Dictionary

כרת כור כרה כרר

The three forms כור (kwr) and כרה (krh) and כרר (krr) are formally unrelated but they all seem to have to do with something round, usually purposed to contain something. The verb כרת (karat) describes a cutting off of what was rounded up.

כור I

The root כור (kwr I) isn't used in the Bible as verb, but in Arabic it means to wind about (in order to make a turban). BDB Theological Dictionary proposes that in Hebrew this verb may have had to do with being round, but it obviously emphasizes containment. Its extant derivatives are:

The masculine noun כר (kar), which is used only in Genesis 31:34, where Rachel stores the household idol in it. It's usually translated with camel's saddle or saddle basket.
The masculine noun כור (kur), meaning smelting pot or furnace (Deuteronomy 4:20, 1 Kings 8:51, Jeremiah 11:4).
The masculine noun כיר (kir), meaning cooking-furnace (Leviticus 11:35 only).
The masculine noun כיר (kir) or כיור (kiyor), meaning pot or laver. This word is used to describe a cook pot (1 Samuel 2:14) or a fire pot (Zechariah 12:6). This noun is also used for the bronze laver of the tabernacle (Exodus 30:18) and those of the temple (1 Kings 7:38), and even for the mysterious bronze item upon which Solomon kneeled and prayed (2 Chronicles 6:13). This word is usually translated with platform, but it was probably more like a bowl or a dish.

כור II

Root כור (kwr II) is also not used as verb in the Bible. BDB Theological Dictionary suggests it may have had to do with to bore or dig, which brings it in close proximity to the previous root. Its Biblical derivatives are:

The feminine noun מכרה (mekora) or מכורה (mekurah), probably meaning origin. It's used only three times in the Bible, all by Ezekiel, twice to describe the origin of Israel (Ezekiel 16:3, 29:14), and once what seems to be Ammon (Ezekiel 21:30). HAW Theological Wordbook of the Old Testament lists this word both under this root and the next.
The feminine noun מכרה (mekera), which something that can be done with a sword (violence? Genesis 49:5 only).

כרה I

The verb כרה (kara I) means to dig. Its object might be a grave (Genesis 50:5), a well (Genesis 26:25), a pit (Exodus 21:33), even a calamity (Proverbs 16:27) or ears (Psalm 40:6). Its derivatives are:

The feminine noun כרה (kara), meaning cistern (Zephaniah 2:6 only).
The feminine noun מכרה (mikreh), meaning pit (Zephaniah 2:9 only).

כרה II

The verb כרה (kara II) appears to denote an acquiring by trade. It's used four times: Deuteronomy 2:6, Job 6:27 and 41:6, and Hosea 3:2. This verb as no extant derivatives.

כרה III

The verb כרה (kara III) means to give a feast, or so it is assumed. It occurs only once, in 2 Kings 6:23. It has only one derivation, namely the feminine noun כרה (kera), thought to mean feast, which also occurs only once, also in 2 Kings 6:23.

The verb כרר (karar) occurs only in one context, but from that context (and its usages in cognate languages) it's safe to deduce that it denotes a repetitive, circular motion: to whirl (2 Samuel 6:14 and 6:16 only). Its derivatives are:

The masculine noun כר (kar), denoting a male lamb (1 Samuel 15:9, Amos 6:4, Jeremiah 51:40). BDB proposes that this noun belongs to this root because of the dancing and skipping of lambs. This same noun is also used to describe an instrument of war, in which sense it's usually translated as battering-ram. BDB asserts that this device was named similarly as in English, namely after the butting, but that doesn't seem correct. Lambs don't particularly butt; that's done by adult rams, and those were known by different words. But it nevertheless seems possible that these devices where known from a repeated motion.
The feminine noun כרכרה (kirkara), denoting some kind of animal. It's used only once, in Isaiah 66:20, where it is usually translated with dromedary or camel. HAW Theological Wordbook of the Old Testament proposes "swift beasts".
The feminine noun ככר (kikkar), denoting a round (thing). It's used to describe a round district (Genesis 13:10, 1 Kings 7:46), a round leaden lid (Zechariah 5:7), a circular loaf of bread (1 Samuel 2:36), a round slab of raw metal (Exodus 25:39) or bullion (2 Samuel 12:30). When this word describes material for a payment, the Septuagint translates it with ταλαντον (talanton) or talent.

Dictionaries list two additional nouns of formally unclear origin or relations, but obviously of the same form as the above. Note that the first of these nouns is spelled and pronounced the same as the noun כר (kar), denoting a male lamb, and the noun כר (kar) denoting a saddle basket:

The noun כר (kar) is an unusual word meaning pasture. It occurs only three times, in Psalm 37:20 and 65:13 and Isaiah 30:23. Some scholars derive it from כור (kwr I), saying that this word for pasture denotes a round enclosure. Others derive it from כרר (karar) via כר (kar), meaning lamb.
The noun כר (kor) denotes a unit of volume (1 Kings 5:2, 2 Chronicles 2:9, Ezekiel 45:14). Verbally, it could probably be compared to our modern unit the barrel, and as such be tied into כור (kwr I).

כרת

The verb כרת (karat) means to cut off (and is related to the English word "carat"). It is used to describe the cutting off of people from a larger collective (Jeremiah 11:19), of trees (Deuteronomy 19:5), of one's foreskin (Exodus 4:25). It frequently describes the "cutting" of a covenant (Genesis 21:27), which many understand to have to do with the ceremonially cutting in half of animals (Genesis 15:10), but which rather has to do with a person or people being rounded up and isolated from a larger collective.

From this verb come:

The feminine noun כריתות (keritut), meaning dismissal or divorce (Deuteronomy 24:1, Isaiah 50:1, Jeremiah 3:8).
The feminine noun כרתות (kerutot), meaning beams (1 Kings 6:36, 7:2, 7:12)