How is it possible to break down concrete filling between red bricks without doing much damage to the bricks themselves, preferably without using jack hammers, drills, and alike too much?

Typically recovered brick (used brick) is recovered after normal demolition practices. This means using a backhoe or such to tear down the wall, though this can also be accomplished using hand tools. That will remove most of the mortar through mechanical action with the rest chipped off by hand. This leaves a lot of rounded edges, chips, and gouges in the brick. This is the nature of used brick and is found as desirable traits.

If you want new bricks with straight lines and sharp edges you are better off getting new cut bricks.

If you are simply trying to save money. Recovering the bricks from a wall yourself is only the cheapest option if you are doing the whole thing yourself. But, this is a labor-intensive process.