1) I am on a one-year PGWP. If an employer has lmia for a job, can he hire me?
2) In case such an employer hires me will i be able to get an extension of my work permit i.e., after my PGWP expires ?
You have posted a PGWP query in a Express Entry forum, so you should move it to the appropriate forum.
In any case,
1. Any employer can hire you now based on your PGWP (Open Work Permit) without a LMIA approved job offer. An LMIA costs time and money so the real benefit for an employer to hire you now is that he doesn’t need to invest in either!
2. A PGWP cannot be extended. Your employer shall need to file for your closed Work Permit just before your current PGWP expires.
If you continue working for your employer for at least a year, you may be eligible for the CEC stream of Express Entry or if you have recent work experience of at least 1 year in a skilled job, you may be eligible as a FSW right away. In all honesty, this may be difficult to achieve one year of work experience with a PGWP duration of exactly one year...since you are unlikely to have landed a job the same day you received your PGWP without which you will be unable to attain the duration required.
Assuming you have completed your post secondary credential in Canada (or you wouldn’t have your PGWP anyways), you should have a decent CRS score that will get you an ITA.
So if you can, perhaps the best course of action for you would be to try kickstarting your PR process right away.