Hi
1. You assume wrong, the answer is NO as you don't have a LMIA supported job offer nor is your job supported by a LMO.
Federal Skilled Workers and Canadian Experience Class
A valid job offer has to be:
for continuous, paid, full-time work (at least 30 hours a week),
for work that is permanent and not seasonal,
skill type 0, or skill levels A or B of the 2011 National Occupational Classification (NOC)
and either:
the employer making you the job offer must have a positive Labour Market Impact Assessment from Employment and Social Development Canada OR
you are currently working in Canada in a NOC 0, A or B job on a work permit that was issued based on a Labour Market Impact Assessment, and
you are working for an employer listed on your work permit,
you are authorized to work in Canada on the day you apply for a permanent resident visa, and when the visa is issued, and
your current employer made you an offer to give you a full-time job if you are accepted as a permanent resident.
In other words, your job offer is valid, whether you are working in Canada or not, if your current or prospective employer:
has made an offer to give you a full-time, permanent, non-seasonal job if you are accepted as a permanent resident, and
has a positive Labour Market Impact Assessment from ESDC.
The only time the employer making you the offer does not need to get a new LMIA is when you are already working for them with a work permit that is based on an LMIA.