Don't overthink and don't overcomplicate it.
There's no such thing as applying "using an invitation letter ". She is applying based on her own merits. She can visit her friends, you and whoever she wants. She just needs to show her ties to return.
If you are a representative it's a good practice to use a representative's email, not an applicant's one. Besides, IRCC will use a representative's email by default most often.
Full time study doesn't always mean you need to attend classes 8 hours a day. It can be like evenings, weekends, etc. It's okay to combine it with your full time work and no issues if it doesn't require a study permit.
You can work as per the limits and conditions applied to your current work permit until you get SOWP.
When your current study permit and work permit expire, you will be on maintained status from your application for SOWP.
IRCC is quite lenient towards unauthorized work and overstays within spousal sponsorship applications and it doesn't trigger significant issues, there's a public policy covering that.