Can my company apply for H1B and L1A simultaneously, and follow up with EB1, EB2 filing, basis which visa is approved?

I am currently on L1B extension (which will expire in an year and half). Can my company apply for both L1A and H1B simultaneously (not literally, in quick succession, though both will be open petitions at the same time)?

Provided the answer to the above question is yes, once I receive the outcome of the L1A and H1B, can the company apply for GC under the following scenarios?

Scenario A: L1 A, H1B both get rejected - can my company still apply for EB2, while I have only a year left on my L1B?

Scenario B: L1A rejected, H1B picked, (will only be active in Oct though) - can my company apply for EB2 while I await H1B? Any possibility, the company can still realistically apply for EB1 while I await the actual visa in Oct?

Yes, they can. You need to be clear on your plan to move to H1B, either COS or Consular processing. You can read below.
Green Card is for future employment, it does not matter to have L1 or H1B.