Question about changing visas and work permission.

I am about to switch from an instructor to a student visa and I was given a permission to engage in activities outside visa status form.

The lady did not speak much English and said to fill out some forms and return them and the work permission form was included.

So my main question is can I fill this out now and seek a new job while waiting for my new visa if approved before my CoE is completed/reception of new visa?

Secondary to this, do I need to reapply after getting my new visa and if so can I continue working the same job while I wait for the paperwork to pass?

I have not seen much online about my weird wacked out situation I am in and I keep running into new issues.

Thanks in advance!