1) when you do H1B transfer/application, Labor Dept only cares your pay stubs; as long as your company can pay you month, you are eligible; this is the same as your company lay you off in two month but does not compensate you anything;
2)theoretically the date when you get laid off, you become "out of status"; practically, two weeks would be fine;
3) Your new company just needs transfer your H1B; you can start the new job anytime after your new company starts to transfer your H1B.