The third sub-category ("anyone who clearly expresses an intention to surrender ...") has generated a number of issues - several are commented above in part 1.

CIHL, v. I, p. 989 pdf, refers to a very important limitation on surrenders reflected in US doctrine; The Commander's Handbook on the Law of Naval Operations (NWP1-14M, MCWP 5-2.1, COMDTPUB P5800.7) (1995) (rev. in 2007 without substantial revision to this part):

11.7 PRISONERS OF WAR

Combatants cease to be subject to attack when they have individually laid down their arms to surrender, when they are no longer capable of resistance, or when the unit in which they are serving or embarked has surrendered or been captured. However, the law of armed conflict does not precisely define when surrender takes effect or how it may be accomplished in practical terms. Surrender involves an offer by the surrendering party (a unit or individual combatant) and an ability to accept on the part of the opponent. The latter may not refuse an offer of surrender when communicated, but that communication must be made at a time when it can be received and properly acted upon-an attempt to surrender in the midst of a hard-fought battle is neither easily communicated nor received. The issue is one of reasonableness.
This manual applies directly to Marines (and not directly to Soldiers); but the "reasonableness" test is well attested in UK and US doctrine - e.g., pp. 229-230 pdf:

Specific categories of persons hors de combat (cont.)

The ability to accept surrender under the particular circumstances of combat was discussed by the United Kingdom and the United States in the light of the war in the South Atlantic and the Gulf War respectively.[52]

The United Kingdom pointed out that it may not be possible to accept surrender from a unit while under fire from another position. Hence, a party which “takes” surrender is not required to go out to receive surrender; instead, the party offering surrender has to come forward and submit to the control of the enemy forces.

The United States took the position that an offer of surrender has to be made at a time when it can be received and properly acted upon and that a last-minute surrender to an onrushing force may be difficult to accept. The question remains, however, as to how to surrender when physical distance may make it difficult to indicate an intention to surrender or may subject one to charges of desertion.

The United States also took the position that retreating combatants, if they do not communicate an offer of surrender, whether armed or not, are still subject to attack and that there is no obligation to offer an opportunity to surrender before an attack.
More specifically, the DoD position is at CIHL, v. II, pp. 997-998 pdf:

349. In 1992, in its final report to Congress on the conduct of the Gulf War, the US Department of Defense stated that:

The law of war obligates a party to a conflict to accept the surrender of enemy personnel and thereafter treat them in accordance with the provisions of the 1949 Geneva Conventions for the Protection of War Victims . . .

However, there is a gap in the law of war in defining precisely when surrender takes effect or how it may be accomplished in practical terms. Surrender involves an offer by the surrendering party (a unit or an individual soldier) and an ability to accept on the part of his opponent. The latter may not refuse an offer of surrender when communicated, but that communication must be made at a time when it can be received and properly acted upon - an attempt at surrender in the midst of a hard-fought battle is neither easily communicated nor received. The issue is one of reasonableness.

A combatant force involved in an armed conflict is not obliged to offer its opponent an opportunity to surrender before carrying out an attack . . . In the process [of military operations], Coalition forces continued to accept legitimate Iraqi offers of surrender in a manner consistent with the law of war. The large number of Iraqi prisoners of war is evidence of Coalition compliance with its law of war obligations with regard to surrendering forces.[401]
The report also referred to two incidents during the Gulf War in which there had been allegations that quarter had been denied. The first incident involved an armoured assault on an entrenched position where tanks equipped with earthmoving plough blades were used to breach the trench line and then turned to fill in the trenches and the bunkers. The Department of Defense defended this tactic as consistent with the law of war. It noted that:

In the course of the breaching operations, the Iraqi defenders were given the opportunity to surrender, as indicated by the large number of EPWs [enemy prisoners of war] taken by the division. However, soldiers must make their intent to surrender clear and unequivocal, and do so rapidly. Fighting from fortified emplacements is not a manifestation of an intent to surrender, and a soldier who fights until the very last possible moment assumes certain risks. His opponent either may not see his surrender, may not recognize his actions as an attempt to surrender in the heat and confusion of battle, or may find it difficult (if not impossible) to halt an onrushing assault to accept a soldier’s last-minute effort at surrender.[402]
The second incident concerned the attack on Iraqi forces while they were retreating from Kuwait City. The Department of Defense again defended the attack as consistent with the law of war. It noted that:

The law of war permits the attack of enemy combatants and enemy equipment at any time, wherever located, whether advancing, retreating or standing still. Retreat does not prevent further attack . . . In the case at hand, neither the composition, degree of unit cohesiveness, nor intent of the Iraqi military forces engaged was known at the time of the attack. At no time did any element within the formation offer to surrender. CENTCOM [Central Command] was under no law of war obligation to offer the Iraqi forces an opportunity to surrender before the attack.[403]
350. The Report on US Practice states that:

The opinio juris of the United States is that quarter must not be refused to an enemy who communicates an offer to surrender under circumstances permitting that offer to be understood and acted upon by U.S. forces. A combatant who appears merely incapable or unwilling to fight, e.g., because he has lost his weapon or is retreating from the battle, but who has not communicated an offer to surrender, is still subject to attack. (Persons hors de combat due to wounds, sickness or shipwreck must of course be respected in all circumstances, in accordance with the First and Second Geneva Conventions of 1949).[404]
Again, the thrust goes more to the soldier's perception - and very little to legalistic, hard-line litmus tests.

(cont.)