-Yes.
2) Can I extend H1 for 3 years by using the approved 140 from my previous company?
-Yes, if your H-1 status still has 3 years to go to reach the maximium six years (irrelevant to I-140 in such a case); or if your Priority Date is not current and you meet the reqirement for such extension (related to I-140 in this case).
3) Can I have my new company to sponsor a new PERM?
-Yes, but really not necessary.