Many complexities here, and many things that you will need to speak with a qualified attorney in order to determine. I'll stick to your numbering system, for clarity's sake:
1a. Yes, your employer can begin the green card process for you because the L category allows dual intent - the intent to be here temporarily on a nonimmigrant visa while eventually intending to get permanent residence and remain permanently. Length of time it will take depends upon method used to file, and this depends on the type of job and your background - this requires a professional evaluation by an immigration attorney.
1b. Technically, no, you won't need to change to an H-1B as a legal requirement - because, like the H-1B, the L is a dual-intent visa (as explained above). This is true for L-1s and L-2s. HOWEVER, it might make sense to do this from a timing perspective, to keep you and your spouse here long enough for the green card case to go through. The H-1B offers certain extension options which the L does not. This is an analysis which you need to go through with an experienced immigration lawyer.
2a. Normally, your spouse would be able to get a green card along with you, and so once you get your green card he would have one as well and could change employers as a permanent resident. Once the second stage of the green card case, the Adjustment of Status (assuming this part is processed in the U.S.) is filed, we normally file for an EAD (Employment Authorization Document along with it, which generally comes through in three to four months from the filing. At that point, even before green card approval, your husband would be able to switch employers. HOWEVER, the timing of filing of this stage of the green card process and whether filed here or abroad depends on a great many complex factors, one of which is the method of applying for the green card (but also including immigration history, nationality and other factors). Only a discussion with a lawyer will be able to provide an analysis of the timeframes involved - and even then this will be only a highly educated estimate.
2b. If he processes along with you for permanent residence, he will be a permanent resident ("green card" holder). If not, he would still have the L-1 as long as that is still valid, or any other status he changes to.
Hope this helps.
YOU WROTE: Conversion of L2 visa to green card: 1. I presently have an L2 visa.
a. Can my employer apply for a greencard for me - how long does it ususally take to get a green card for L2 visa holders.
RESPONSE: Yes, your employer can apply for you. Remember that the green card application is "prospective in nature". This means that the green card application has to do with what will be going on when you get the green card and not right now.
YOU WROTE: b. Will I first have to change my visa status from L2 to H1B prior to applying for the greencard.
RESPONSE: You do not have to do that but there may be some advantages to doing so. For example, there is a cap or limitation an an annual basis with regard to getting H-1Bs for some people so the sooner you get it may be better for long term strategic planning for the green card process.
YOU WROTE: 2. My spouse presently holds a Blanket L1A visa and therefore is restricted to work only for his sponsoring company. Once I get get my Green Card a. will my spouse be able to sitch companies and begin working on an EAD
RESPONSE: Once you and your spouse have green cards you can engage in "free market employment". THIS MEANS YOU CAN WORK ANYWHERE. However, please note that the green card process by an employer contemplates that it is for a particular job with a particular employer and that this intention needs to be maintained by the employer and the prospective employee throughout the green card process.
YOU WROTE: b. What visa status will he hold if I have a green card ?
RESPONSE: You will be a lawful permanent resident in the U.S. Please feel free to contact our offices at firstname.lastname@example.org for more information as these responses to your queries cannot substitute for competent legal advice about your particular case.