Yes, it's perfectly fine English but is heavily nuanced.
"It would seem" expresses an opinion about the current state of something:
It would seem that we are out of milk
This is roughly equivalent to "I think we are out of milk". It also frequently implies the question of whether the situation is true, to which the listener could respond something like:
Yes, it would seem so.
to mean they agree with the opinion. In addition, the expression is relatively polite since I have expressed my interpretation of the situation rather than saying it is definitively true.
You don't have any money.
It would seem that you don't have any money.
I might know that you have no money, but by saying "it would seem" it sounds more considerate.
Lastly, the expression reflects the famous British characteristic of understatement in the face of bad news or adversity, to make the situation seem less dangerous or perilous than it actually is.
Well, old chap, it would seem we are surrounded by hungry tigers with no hope of rescue. Might as well break out that whiskey you've been saving, eh?
"Our situation is even worse than we had feared" is also fine. It says that the current situation -- implied by the "is" -- is worse than we previously thought it would be.
You are correct and the "had" is optional, but using it does imply that, at some previous point, they did seriously consider the situation.
Ah, it would seem the situation is worse than I had previously thought. In addition to the tigers, the tree we are in is infested with venomous cobras. We may as well finish the bottle then, what?