Moving the primary home

[Pandu Chimata]

Hello team, I currently own a house and been living since 13 years. Its time to downsize as kids moved out of the house. 

If I buy another house/condo, smaller than I live currently , would that be considered as a primary home? How does the lender treats my next home as a primary home and what kind of documentation I need to provide for that?

Another question is - If I buy that house or condo in cash (off market for a quick close), and then can I turn around get a mortgage as a primary house, obviously keeping 20 to 30% equity in the house? 

Please help me address the above two questions. Appreciated.