No, the L-1A visa ties your employment to the U.S. affiliate.
Yes, any person can start a business in the U.S., however, only persons with proper authorization to work in the U.S. can be employed by that business. When you receive your L-1A, you can only work for the business which was the basis for your L-1A.
The transferring employee may bring a spouse and any unmarried dependent children under the age of 21, upon approval of their L-2 visa application.
Spouses of L-1A workers now automatically have unrestricted work authorization ‘incident to status’ without needing to apply to USCIS for any employment authorization document. Proof of that work authorization will be placed in the spouse’s I-94 as “L2S”.