[RPG] Can a Fire Elemental deal damage to multiple creatures in the same turn by moving into their space

Yes, but they don't stack.

PHB 206:

The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect—such as the highest bonus—from those castings applies while their durations overlap.

For your specific case, having two Walls of Fire in the same space does not double the damage. However, if it was a Wall of Fire and a Cloud of Daggers, those effects would overlap and targets in the area would take damage from both.

To answer the title question, nothing prevents the second Wall of Fire from being cast on top of the first, but it wouldn't add extra damage.

Creatures can be thrown through the walls, but would have to make the saves one at a time as they attempt to pass through them. Willingness to do so doesn't matter, unless specified in the spell.

I believe the wording is made in that way because a creature might not pass through all of the walls, because they're stopped short by an effect, leaving the rest of the walls up. I don't believe that the wording means you must intend to go through the walls to be affected by them, rather, you attempt to make it through all of them because there is a chance you might be stopped (or killed).

You make the saving throws one at a time, as you pass through it. You might pass through every wall, eventually, but only one at a time. Imagine time slowing down for each save, because the effect from the first might prevent you from traveling through the second.

Another thing to consider, most of the spells in the game specify if the creature needs to be willing or not. A quote supporting this from an unofficial source, lead rules designer Jeremy Crawford:

A spell specifies whether a target must be willing. If it doesn't specify that, the target doesn't need to be willing. #DnD