(1) Generally, L-2 status is valid only if the dependent is accompanying or following to join the principal beneficiary in the United States. "Parking" (actual term used by the USCIS) of L-2 dependents is not permitted while L-1 principal is stationed outside US, however, if your absence from the US is for a brief period and just for obtaining an L-1 visa, your wife can stay and work in the US.
(2) Yes, she can use the existing EAD if you are coming to work for the same employer.
(3) Yes, if her prospective employer files for change of status from L-2 to H-1B.
1) I agree with Rajesh. He has perfectly summed it up.
2) Yes, she was work a long as the EAD is valid
3) She can switch only if change of status is approved towards each filing. For H-1B the employer will seek COS by filing the I-129 petition and upon approval she will join H-1B employing petitioner and when she wants to switch back to L-2 she will filed I-539 and upon its approval seek EAD to work.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. If you would like additional information based on this response, please contact my office at 510 657 7665 or 415 902 0832 to schedule a consultation.