Sponsor / invitor question - Job Changing Question

[praghura]

Hi there,
I guess I confused you with too many questions.
here is my simplified mail

Question1:
Can I just invite my parents without sponsoring them?

Question2:
Is the sponsor changing jobs between applying for a VISA interview and the actual VISA interview any problem? Not even received the H1B. Just joined the job and interview is in three weeks. Any issues with that?

Will be very grateful if you clarify.

[praghura]

Correction

The statement 'not even received H1B' is not quite right.

I should say that the transfer of H1B is submitted and approval has not come.

THANKS MUCH
Please help.