How long does it typically take to process an E-2 visa in London?

It all depends how busy the E-2 department at the consulate is. Typically it has been taking 2-4 months.

Will our age diiffrence be a problem to get the legal status for her.

The age difference may be raised but if you can establish that it's a bona fide marriage, then they will approve it.

If the part time H-1B is denied after RFE,etc. would that cause a problem for already approved full time non profit H-1B?

no - this is would not be an issue.

If i initiate GC will i be eligible for EB1 category, even though on L1B visa?

What I have successfully done in the past is switch from an L-1B to an L-1A (if one qualifies) and then file the EB-1 case. No need for labor...

You should wait to file the I-130 and I-485 together when you naturalize.

How do I need to prove that the home residency requirement doesn't apply to me on J-1, when applying for an E-2?

if on your J-1 visa it does not state that you are subject to the 2 year foreign residency, then there is no issue and no need to document this.

EAD

If you do not get your card within 90 days then you can make an Infopass appointment to check on your case. Volunteer work is permitted without...

Does my passport need to be valid for the full duration of a non-immigrant work visa?

You can use your old passport along with your new passport to show the validity of your status until mid-2018

Applying for green card for spouse

You can file for his green card now. You will need to establish that it is a bona fide marriage. You should begin collecting joint documents for...

Recently my wife's I-539(COS) has been rejected by USCIS-her previous status has been expired a year ago. Please advise.

It would appear from the facts presented that she continues with her F-2 status after the denial.