In D&D 5e, is casting wall of fire like this allowed, or would I need to have line of sight for the entire corridor? Assume my wizard knows that the corridor extends both ways and how long it is.
If you are speaking of the spell Wall of Water, this case is covered in the description of the spell:
[...] fire damage is halved if the fire effect passes through the wall to reach its target
Yes it would work, but the damage is halved.
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.