You should never lie to the CIS. I would recommend talking with a local attorney to represent you after a review of all the facts.

I missed my oath ceremony because i was sick

I agree with Attorney Barlow.

CIS will reschedule but to take a long time. You can call the CIS to ask them to reschedule sooner.

E 2 visa substantial investment amount

E2's investment depends on the type of business. What type of food business are you planning to open?

How long one can remain in USA after submitting the J1 waiver petition in Sept 30, 2013 if the J1 visa is valid upto 30th Nov ?

You should discuss this with the attorney who is handling your case.

Will EAD on L2 expire if L1 visa of spouse expire in Jan 2014, but I-94 on L1 is valid till 2016?

Your EAD should be based on when your husband's L1 I-94 expires.

Will it jeopardize husband's status if he declares greencard lost and change his address upon returning to USA?

You should consult with an attorney. Generally you can file to have another green card issued to you. However, something else seems to be going on...

Can I transfer my H1B to new Employer & still continue GC process with old Employer?

Hi Krishna, Yes to both, as long as your previous employer is willing to keep the green card.

DV Lottery related question:

There is a 3 or 10 year bar from re-entering if you overstay. If you overstayed beyond 180 days and left voluntarily, the bar is for three years....

I`m under U Visa if I married with a Canadian citizen + Portuguese citizen can he work here? Can I get the papers for him

You should consult a local immigration attorney to help you.