combination of fighting units , smaller than a division ?

Answer 1

The US Army is composed as follows. Most world-class armies have a similar scheme.
Above division, you have:
THE Army -- the whole thing, not a fighting command, but serving to recruit, train, equip, and administer the force. headed by the Army Chief of Staff (4-star general).

An Army Group -- composed of 2-3 separate armies. Not used since WW2. Headed by a 4-star general.

An army, called by a spelled out number: Third Army (Patton's command) Eighth Army (Korea), etc. Composed of 2-3 corps, plus special army-level units. Headed by a 4-star or 3-star general.

A corps, composed of 2-3 divisions, plus special corps-level units. Corps are given Roman Numerals: VII Corp, V Corp, etc. Headed by a 3-star general.

A division: Composed of normally three brigades plus special division-level units. There are different types of divisions: armored, infantry, airborne, airmobile. Divisions are numbered by type and usually have a unit name: 1st Infantry Division "The Big Red One"; 82nd Airborne Division, "All-American" etc. Headed by a two-star general.

The brigades in the division contain most of the Army's fighting units (battalions), plus separate brigade troops. Brigades are numbered within the division, "1st Brigade," "2nd Brigade."
Brigades normally contain three battalions. These may be a mix (say, 2 armor battalions and 1 infantry) or all the same. headed by a 1-star general or a colonel.

>> There are also regiments. These are special-purpose units, such as cavalry (7th Cavalry Regiment), headed by a colonel, or formal, but not organizational designations used used only to trace military lineage. For example, my old unit, the 4th Battalion of the 35th Armored Regiment was part of 1st Brigade, 4th Armored Division. The rest of the 35th Armored Regiment was elsewhere.

The fighting battalions are of one type of force, although there will be a mix of weapons in them. Plus, it will have other special units to suport the fighting units.Thus, an armored battalion has three tank companies; an infantry battalion has three infantry companies. In peacetime and garrison, the battalion stays together. During actual military operations, the brigade commander will often cross-attach (switch around) companies in his battalions to "task-organize" the forces for the job at hand. Thus, an armored company may be cross-attached to an infantry battlion to give it greater striking power. Battalions are lead by lieutenant colonels.

A company is lead by a captain. It is composed of three platoons of the same type, plus (for infantry) a weapons platoon with bigger firepower. In combat operations, platoons of different types may also be cross-attached between companies.

A platoon is lead by a 1st or 2nd lieutenant or sometimes, due to shortages, a senior sergeant. An armored platoon is all-tanks. An infantry platoon has three squads and, normally, supporting machine-gun teams.

The squad is lead by a sergeant and has two fire teams, each lead by a sergeant or corporal.

There are, roughly, 4-5 soliders in a fire team, 10 in a squad, 30 in a platoon, 100 in a company, 400-500 in a battalion, 2,000-3,000 in a brigade, 10,000-12,000 in a division. There is often a difference between the assigned number of troops on paper and the actual number in the field.

Special, suporting units are "organic" to different levels, but may be "loaned" to subordinate commanders for operational purposes. At lower levels, you have mortars, medics, etc.
Higher, you will have signals, artillery, aviation, intelligence, doctors, transportation, supply, etc, etc.

At the very bottom you have the individual soldier, with his individual or crew-served weapon, tired, dirty, carrying enough weight to kill a mule, wanting to be anywhere else, but doing his job.

Answer 2

There is a squad or a team.

Answer 3

See diagram.