How long could the written decision take after a hearing?

It may take weeks to months. An EAD withou advance parole does not authorize travel.

How much time will it take to change my visa status from J1 research to J1 clinical inside the us?

If your I-94 is valid for d/s duration of stay, you only need 2019,. If you need to file expect 3-5 months processing time.

When can I apply for my permanent Resident Card?

Within 90 days of expiration date.of conditional residence

Is it worth me asking for a motion to reconsider for a h1-B denial?

Appeal is recommended if you want H-b unless you have other options.

As my colleague recommends, follow the form instructions closely.

In part 5 of I-864 do i need to mention my wife in my son's form and vice versa ? I will be filling different i-864 for them.

If you are a sponsor of both they need to be listed

Will I be able to re-file I-485 i-130 forms for my spouse after being denied at the first time?

If the petition and application were denied because they were filed before you were married, yes you may refile. If it was denied for something...

Is my brother student F1 visa still valid when university terminate his SEVIS ID?He is still in india. Got visa for first time

Yes the visa may be canceled if DOS notified. Apply for a new visa.

It is the case number for the Immigrant visa

it may be fastest if you do not marry and file a K-1 and complete the process in the US. Otherwise you need to file the immediate relative petition...