2. Not LC, it's EAD from I-485 filing (c9 based), unless you can get EAD under other eligibility (such as c5, c8 ,a17,...) or visa class that allows you to work for petitioner(such as H1, L1, O1,..)
3. PERM is the way now for new filer. People get approval (or denial) within 1 or 2 months after on-line submission.