I want to apply visa for my wife and they have 2 minor child

Assuming you are a U.S. citizen not permanent resident, no You must file separate petitions for each of them as your wife and each step-child. ...

You should definitely have the basis for your asylum application reviewed. Yes, it may very well affect your asylum case. In an asylum case you...

If someone was denied entry on a tourist visa, does that cause a problem obtaining a K-1 fiance visa?

No. Assuming she meets all requirements and is admissible, it won't affect the K1

Applying for mothers visa to come to the States with sibling?

Unfortunately, the law does not provide for that. Either you need to petition for your brother separately from your mother, in which case he needs...

Can I file I-821 while I am in H1B cap gap?

TPS is an indefinite status that sometimes goes on for many years--provided you registered during the initial registration period. You should...

No, the adjustment will be adjudicated separately. However, advance parole is not for leisure travel.

Unavailability of record CFR 103.2 (b)(2)

You can have your mother get to work to obtain it, file using the abridged version, but expect a Request for Evidence for the long version. You...

Should the copy of birth certificate be unabridged or abridged? For the I-485 package?

They require the long form that has not only your birth data but also the data of your parents.

Yes. You must acknowledge paternity. Is your name on the birth certificate as the father? It will be harder later on for the child to...

F4 beneficiary and their spouse

The original I-130 filed all those years ago expressly asks the names of the beneficiary's (your dad's) spouse and children. Given that you say...