In the scope of a new employer: When H1b transfer is submitted that in Premium, can an H4 transfer be attached to it and would it get premium processed too? In the scope of the same employer: Also, is H4 valid (within its i94) as long as the underlying H1 is valid, even though I'd have to file H1 extension/amendment?
There's no H-4 premium processing anymore because all H-4 extensions require biometrics now. You can file concurrently but the H-4 will not receive premium processing. H-4 status remains valid as long as the I-94 has not expired and the principal maintains H-1 status, even if the H-1 principal changes employers.
You sure about the last part? Employee transferring, shouldn't the H4 have some kind of amendment?
You can file both at the same time, but there is no premium for H4 or /EAD Yes
To your first point, wouldn't they generally adjudicate the H4 together with the H1?
They can. And, yes ideally that's the expectation. When we filed earlier this year, all our docs (H1B , H4, EAD) all got approved on the same date. But I have heard some friends who applied but the H4 and EAD came a bit late.