Here are my opinions on your questions. Your wife is now in H-1B status and her L-2 EAD is no longer valid. She does not need to do anything else to validate her H-1B status until she departs the US. She will then need to obtain an H-1B visa from a US consulate abroad before she can reenter the US in H-1B status. She will not be able to extend her EAD unless she applies to change her status back to L-2. The two of you should meet with an immigration lawyer in person to review your individual cases, get your questions answered, and plan appropriate actions. See the link to the American Immigration Lawyers Association below for help in finding an immigration lawyer near you.
An attorney must review your paperwork to give an accurate answer. I suggest you ask the attorney who filed the H1b.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
If the H-1B was approved with a change of status, there's nothing more she needs to do until the next time she travels abroad (at which point she will need to get an H-1B visa stamp at a US consulate abroad in order to return).
Since she is no longer an L-2 in this situation, she is no longer eligible for an EAD and can't renew it.
Speak with an attorney for further guidance.
If the H-1B indicated a request for change of status and the I-797 approval notice indicates her status change was approved effective on or before the day she started work, she is now in lawful H-1B status. As such, her nonimmigrant status is not dependent on your L-1A. She can not be in 2 nonimmigrant categories at the same time so she is not an L-2 and cannot get an EAD as an L-2 if the conditions in the first sentence above exist.