I am about to travel tonight [Saturday] but noticed my I have lost my green card...what can I do?

So not travel unless you can get an info pass and have a stamp plAced in your passport

Immigration question

If you sponsor your brother it will take at least 10 years before he can get a visa to come here

J1 waiver at a VA hospital. H1B is cap exempt if you file while in USA but is it subjected to cap when done outside USA?

An h1b visa is subject to the cap or exempt from the cap regardless of whether you apply here or at the consulate. Consult an attorney to...

A visa denial or refusal of entry could delay application or result in a denial. A b visa is non immigrant intent and a K visa is immigrant intent...

Form I-130. Place of birth.

Write current name formerly known as

PD is current. Is there an expiration in the application to adjustt status?

There is no expiration but you may lose your priority date if visas retrogress to earlier years

Fee waiver for court costs based on section 8

No it will not qualify you for a fee waiver

Green card/ visa through employer

It will be hard. You will have to consular process and apply for a waiver. Consult an attorney

Would immigration approve him considering our 5 Year age difference?

Yes he can be legalized but would need to file a waiver for his unlawful presence and have an interview at the consulate in his home country

Yes you can if you qualify for L1 status