The phrase "and yet it appears" is correct and usable in written English.
It can be used to introduce a contrast or an unexpected outcome in a statement or argument.
Example: "The evidence was inconclusive, and yet it appears that the theory holds some validity."
Alternatives: "however, it seems" or "still, it looks like".
And yet it appears Dickens was wrong.
And yet it appears she is doing just that.
And yet it appears that the public presentation of the Syria evidence will be limited.
And yet, it appears they are being decidedly cautious about their newly won freedom to advertise.
JUDGE: And yet it appears that in October of 2015, you unfriended the plaintiff?
And yet it appears to be the settled view of every pundit and psephological expert that they are once again about to hold the balance of power.
I couldn't begin to imagine where some of that had come from because it didn't always appear to have a logic, and yet it appeared to me to have its own innate logic.' That element of the unconscious crops up repeatedly in our conversation.
My aching muscles – most of which I didn't know existed until now – are waving white flags and, somehow, I have a mouthful of dried mud and grass, yet it appears I have only been doing this for 28 minutes.
For example, the first orphan receptor-ligand pair to be identified was 9-cis retinoic acid and RXR [10], yet it appears unlikely that sufficient 9-cis retinoic acid exists in vivo to serve as a true endogenous ligand [18].
This is a key point since NEP metabolizes a number of vasoactive peptides, such as endothelin-1, bradykinin, and vasoactive intestinal peptide (Campbell, 2003), yet it appears that it is primarily the enhancement of the cytoprotective effects of natriuretic peptides that underpins the efficacy of combination treatment in IPF.
Yet it appears the apology was insufficient.
