My new job at the consulting firm has asked me to fill W-9 form. Should I be filling it?

Yes, you are required to complete a form I-9.

Apply for asylum by someone his green-card application is denied

He will not be within the one year deadline to file for asylum, so he can expect to be placed in removal proceedings. Courts look with great...

Will I be deported?

As of now, generally DUI is not a deportable offense, however the specifics are very important and it could amount to a crime involving moral...

F2 Dependent Visa

She can apply now for an F2 since you are in fact married.

I94 extension for H4 dependents.

Yes, file an H4 extention for them.

Can someone be bailed out at all when ICE has a hold on them?

If ICE sets bond, you can. If he is not yet in ICE custody, you should post bond and get him into ICE custody. It's good to have a hearing...

What is the best option of a PR to get immigrant visa for his indian unmarried son aged 25 at the earliest ? How long it take?

You can file an immigrant visa petition for him. there is an 8 year wait for F2B category [son over 21 of LPR from India]].

Derivative asylee status for h1B holder

she can file an I-730 for you, yes. One year later you can file for adjustment.

What are the legal obligations of sponsoring immigrant/

She is required to keep the sponsored immigrant at 125% of the poverty rate.

No, only if the visa is currently available and 4th preference is not.