If my U visa application is filed by this week, can I get my U visa considered for quota in Oct 2014?

Not likely since it normally takes at least a year.

Can someone fix papers by the time living in the us

Possibly. Check with an immigration attorney if they qualify for DACA.

Work during L1/L2 visa extension

Ask the employer's immigration attorney.

Divorce and immigration status hits on K1!!

Contact an immigration attorney to assist you in preparing a waiver if applicable of the joint filing requirement on the I-751.

Green card lost

Do you still have the approval notice? It could help to get a replacement document. Contact an immigration attorney for more.

File an amendment with USCIS referencing the receipt number and explain the change. It may be a good idea for you to have an immigration attorney...

Travel to US three months before H1B expires

1) no 2) yes as long as I-94 is still current when filed

1) yes as long as you continue to fulfill the H1B requirements 2) the school can tell you this. Consult with an Immigration attorney for best results.

Will change of job require re stamping of existing valid H1B visa

You will need an unexpired one.

How to answer question 11 on Form I 485 ?

Since you were granted asylum this would impact your details and therefore your answers. You no longer need to comply with the FR requirement. I...