[RPG] If a character is stunned but still has attacks remaining, can they still make those attacks

Yes, a Battle Master can give up their single-attack Attack action to use Commander's Strike.

You appear to be confusing the Attack action with an attack.

The Attack action is one of the things you can choose to do with your action; others include the Dash action, the Cast a Spell action, and the Use an Object action.

An attack is anything you do that causes you to roll a die to overcome someone's AC. Trying to hit with a weapon is an attack, but so is using a spell that rolls against AC, such as eldritch blast. You can make attacks without taking the Attack action, e.g. attacking with a spell using the Cast a Spell action, attacking with a magic item using its own unique action, or attack with a weapon using a reaction (e.g. using the Ready action, or making an opportunity attack) or bonus action (e.g. from Two-Weapon Fighting).

The prerequisites for the Battle Master fighter's Commander's Strike maneuver are that you:

• take the Attack action, which always allows at least one attack, and
• forego one of those attacks, even if it is the only one

The rules for grappling and shoving a creature are similar.

Your players have a lot of options.

From the Grappled condition:

• The condition ends if the grappler is incapacitated (see the condition).
• The condition also ends if an effect removes the grappled creature from the reach of the grappler or grappling effect, such as when a creature is hurled away by the thunderwave spell.

So any method of inflicting the incapacitated condition on the mind flayer will end the grapple. Likewise, anything that gets the barbarian out of the mind flayer's reach will also end the grapple. There are far too many ways of achieving these to list here.

It's also worth mentioning that, since the Extract Brain ability requires the mind flayer to use an action, preventing the mind flayer from taking actions would also work. Most of the methods to do this would involve inflicting the incapacitated condition, and therefore end the grapple anyway. But as an alternative option, there's always mind control. There are a large number of spells that could be used to persuade the mind flayer not to extract the barbarian's brain, or just to let them go.

Since the mind flayer's grapple requires a Medium or smaller creature, polymorphing the barbarian into something Large should also free him. There is a minor point of ambiguity here - while the grapple can only be used on a Medium or smaller creature, it doesn't technically say anything about what happens if a grappled target becomes Large. But I think most DMs would agree that this should work.