Yes - a prospective employer can file an H-1B petition on your behalf.
Disclaimer: The information provided here is generalized and should not be relied upon as legal advice. This communication does not create an attorney-client relationship.
An employer can file an H-1B petition on your behalf but you must have status until 10/01/13 in order to change your status to H-1B. A pending extension request is not enough if not approved by the time the H-1B petition is adjudicated. You would have to leave the US and apply for a visa to obtain H-1B status.
It depends. Currently, there are no H1B visas available until October 1, 2013, but you can file as early as April 1, 2013. The USCIS often runs out of H1B visas on the month that you can apply, so this should be started soon.
If you're L visa is denied, then this can create issues regarding the validity of the change of status, since you are waiting for a pending L1.
In addition, you're no longer arguably going to remain in status if the L is denied before or after the H is approved. However, if you have a valid I-94 for the new H1, then this certainly should help you. Good luck.
This is general information, not legal advice, and does not create an attorney client relationship.