Can a Pit Fiend summon from an Infernal Hexblade's Greater Summon Warlock's Ally pick up (or be given) a magic sword and use it (without proficiency) as a basic attack, like characters from any class can?
Summon Warlock's Ally creates a summoned ally with a very limited scope of actions.
It is not possible to pass a summoned pit fiend shadow a weapon, or have it use that weapon to make basic melee attacks. The Summon Warlock's Ally power states, in part:
The creature lacks actions of its own. Instead, you spend actions to command it mentally, choosing from the actions in the creature's description.
Heroes of the Forgotten Kingdoms, page 213
A pit fiend shadow is detailed on page 236 of the same book. It can make a melee attack as a standard action, a tail swipe to cover the warlock as an opportunity action, pulse its fear aura as a minor action, and walk/shift/stand/run/squeeze/crawl once a round as a minor action. These are all the actions available for the warlock to command it to use; it has no other actions.
There is no entry in the description that lets it take a melee basic attack, so it cannot. (It is described as wielding a weapon, but its melee attack has a fixed damage expression instead of using [W].) There is also no entry for many common actions that player characters could take, such as picking up an item or drawing a weapon; technically it can't even do things that require free actions, such as talking.
4E tends to very sharply delimit the use of powers, especially combat powers, extra-specially combat powers that summon another combatant. You're free to hack or otherwise make judgment calls; for example, I'd let any summoned ally take the escape action as a minor, which seems like an oversight.