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.
Strict RAW can be read this way but is confusing
One side of the wall, selected by you when you cast this spell, deals 5d8 fire damage to each creature that ends its turn within 10 feet of that side or inside the wall. [...] The other side of the wall deals no damage.
A big part of the issue here is that the phrase "side of the wall" is not well-defined. It can refer to both an undefined area created by the wall's presence and also the physical surface of the wall itself. Both readings cause issues for this spell, RAW.
Side of wall = area reading
This is the way most people seem to want to read the spell (myself included). Unfortunately, a close reading reveals that reading it this way actually makes no sense with the way they chose to word it.
The problem with reading the phrase as being indicative of the area created by the wall's presence and not the physical surface of the wall is that it makes the phrase "within 10 feet of that side" make no sense. How can you be within 10 feet of an area that isn't even defined? Reading it this way, the spell doesn't even seem to work since there is no way to adjudicate where the effects are. Because it makes the spell not work at all, this cannot be the correct reading.
Side of wall = physical surface reading
Using "side of the wall" to mean the physical surface of the wall makes this clear. However, it then creates an issue that the area on the other half of the wall is technically within range of 10 feet of the surface of the wall.
Nothing in the description says that the other side dealing no damage strictly is meant to cancel out the clause in the first sentence which says that damage is done "within 10 feet of the [damaging] side". And technically 9 feet of non-wall space on the "non-damaging" side of the wall is within that range.
That leaves a narrow 1 foot segment on the "non-damaging" side that a creature would not take damage on.
The RAW is unintuitive and confusing, and I've never seen it played that way
While by a very strict RAW reading the above ruling could be called correct, I do not think it would be wise to run it that way. At the very least, I would not and have never run it that way and I think doing so would be a bad idea at most tables.
Firstly, by the RAW reading the phrase saying the other side deals no damage has almost no use whatsoever. It creates a small 1 foot gap of safety and that is it. This is not even enough for a creature to stand in. This seems unlikely to have been the intent of the spell (though I have no proof of this). If it had been intended, the designers could have written this so much easier by omitting the safe side verbiage entirely and having damage radiate from the wall 10 feet equally in both directions.
I do know that when players and DMs (every one that I have played with) read that they can make one side of the spell "[deal] no damage" they rightly expect that that side of the wall is safe for them to be on (eg "creatures on this side of the wall take no damage").
I think this is a good, natural reading for the spell and I think the RAW is straining quite a bit. Running it by RAW is a jarring diversion from this reading and this could cause confusion and arguments at the table.
The RAW also would increase the damage potential of the spell by quite a bit. Now the damaging area of the spell is almost double. This does come with the tradeoff of making it much harder for the players to use the wall for protection on one side of them in cramped areas (without taking damage themselves). It also makes it more difficult to avoid damaging allies.
Personally, I think that the RAW should be disregarded here in favor of the more common and natural reading of the spell, but your table should do whatever is the most fun for them.
Best Answer
The wall is opaque but doesn't otherwise stop attacks.
Since the wall of fire is opaque, creatures inside can't be seen. Thus:
(PHB, p. 194)
This means:
Melee and missile attackers make their attacks at disadvantage.
Creatures on one side of the wall may roll a Dexterity(stealth) check to become hidden to foes on the other side of the wall, requiring attackers to guess which locations to target with their attacks.
Nothing in the spell description specifically says that making attacks through the wall will inflict damage on the attacker.
Nothing in the spell description specifically says that grappling or shoving are affected.
However, the description of wall of flame does say that a creature who "enters the wall" takes damage. A DM could quite reasonably rule that grappling, shoving, and making melee attacks with some weapons (short ones) constitute "entering the wall", and impose damage in those cases.
Any spells that target a creature or point that the caster can see cannot target inside the wall of fire.
Spell effects extend through the wall (the description of wall of fire doesn't say that they don't), so spells that affect an area that originate from outside the wall can affect creatures inside it normally.
Note that many spells that are attacks (for example, fire bolt), don't target a creature the caster can see, just one within range. So these spells can be used against creatures inside the wall, but, just like missile attacks, they will be made at disadvantage (or just miss outright).