Regarding your question around becoming a Legal Permanent Resident (LPR, that is, a green card holder): The L1B non-managerial category usually processes slower than L1A (senior managers and executives). This is most often because L1B holders fall under the EB2 (employer-based, 2nd priority) permanent residency category. If your employer's immigration lawyer has the experience to do so and sees that you meet the definition, see if you can get classified as a "functional manager" (meaning that you are primarily responsible for a critical part of the business), which would put you in the L1A visa category and give you a much easier path to EB1 LPR status. Note that L1 visas, whether A or B, have a general cap of 5 or 7 years before the holder must leave the United States.

Your employer applies for LPR on your behalf. When using employment- or investment-based visas, you will quickly find that all paperwork has to be done by your employer or corporation and you're just along for the ride.